Sounds like a partial vapour lock situation . Often can happen when fuel is low in the tank and engine heat can be absorbed by the fuel within a section of fuel line prior to the carb . The static head of fuel in the tank cannot over come partial fuel vapour lock within the fuel line . Does not happen often . Usually more often when hotter ambient temps low fuel and short term shut down allows the Perfect Storm Theory ! P.S. If not a believer in the Perfect Storm Theory ? Then perhaps your auto choke system is becoming sluggish .Next time this occurrs or you notice a bad idle for more than 1 to 3 minutes after initial start up , immediately check the butter fly position on the choke . It may be partially closed causing a flood condition on a warm engine , causing the no start condition . This would also explain the wetness on the rubber of the air filter .These GCV Engines with the auto choke mechanism will begin to bind after 4-6 yr period from dirt and grime along with moisture , A simple degreasing and light lubrication will often free them up .

Good advise on the choke. Though on yours, it is in the serial range where they had some defective choke controls /thermowaxes. It's basically pulling the carb and thermowax piston thingie and replacing it. I set the thermowax w/ some Hondabond though.

Auto Choke Pull Off linkage Tom , very similar to the old Thermostatic automobile systems of the 70,s prior to the electric / vacuum units . Sometimes the wax filled bellows is not at fault but rather the metal linkage that becomes corroded and binds sporadically . The op,s pic shows significant oxidation which would further indicate potential for this condition . I have repaired a few Residential Hondas with both causations .

Okay Doc's you're speaking in your doc speak ...what exactly should I do spray carb cleaner on there. By the way I did look and the when I finally got it started the mower was filled with gas so she must have somewhere in there topped it off when it wasn't running ...if that means anything I don't know. And finally I don't understand why shutting the fuel thing off actually was what allowed me to get it started...

Just another potential item , since you again mention the fuel shut off . The inlet needle valve under your carb float maybe allowing a little fuel to bypass and flood the engine , as evident when you stated the rubber filter gasket had fuel on it . Always shut off the fuel valve when not using the unit , apparently Your daughter did not .Your pic shows a little dirt and debris around the engine and carb . Clean the carb linkages and carb internals . The carb should be removed and internals cleaned vigorously for a proper job . Yes , carb cleaner externally and internals . Check utube for proper cleaning procedures for your mower and carburetor ! I think you require video evidence of what we are explaining . Not rocket science but confusing if you have not worked on small engines for numerous yrs . Worse case scenario as Tom advised you may need a new thermostatic choke wax filled module . This unit opens the choke butter fly on your carb when muffler heat expands the bellows after 1 to 3 minutes from start up . If this is over your head bring it to your local repair shop , not a big job , most likely 1 hr shop time !

Ok....true I only ever used shut off at end of year. I can clean outside. Worst case we get it serviced. My experience with carbs is I am better off just putting a new carb on....that's as far as my skill set typically goes. Does a new carb solve the wax thing? If not and it still acts up I think it's off to the dealer....thanks.

The Choke Thermostatic Module is a separate component that attaches beside the muffler and is attached to the carbs butter fly linkage assembly . You may 1st wish to try adding some concentrated fuel cleaner 2 ounces within a full tank of fresh fuel over night . Then degrease the carb linkages with carb spray cleaner then dry and sparsely spray some penetrating oil on the linkages . Then remove the air filter and generally exercise the butter fly open then closed . This may resolve both potential issues , internal inlet needle gumming and external choke assembly binding due to dirt or oxidation . Give it a try 1st , failing this Shop repair may be warranted Bud !

this might help. #24 is the thing that is supposed to adjust the choke. #25 is your choke assembly. that is what they want you to clean sometimes they bind up with muck.

http://peparts.honda.com/powerequipment#/browse/lm/hrr/hrr216/HRR216K8-VKAA

1. Thermal Wax Assembly , otherwise known as a Thermostatiic Choke Module in the Industry .Cleaning will not help . The linkages that apply the laterial linear movement is what begins to bind and require periodic cleaning and lubrication The module will require replacement normally between 3 - 6 yrs of life cycle . Each control module will fail differently , this module can fail open or closed . The Briggs & Kohlers normally fail open . This the complaints of no start when cold They never apply full choke during a failure . Also they do not adjust the choke but should apply full Choke when engine is cold and open choke fully when engine is hot . Let's see what route the op decides upon . Got Your Popcorn Ready ?

The route is simple. First to see if it happens again. Second try to clean things up. 3rd stop in and get an estimate on what this cost to repair and what three or four new wheels cost since I noticed there pretty much ball today. Finally consider trading on something new. I will follow up over the coming weeks. Thank you all so very much.

walk, i didn't say to clean the wax thing! i mentioned the choke assem. was what MIGHT need cleaning. the diagram i supplied is clear.

Popcorn is Hot and Buttered ! Andre warned us this would be a 3 Volume Edition . P.S. Yeah the Carb linkages MIGHT need Cleaning , however it would appear CLEAR from the op,s intro that the air filter gasket is wet from excess fuel which may be a basic or contributing causation of this issue. Buying a new carb when a simple fuel treatment or internal inlet valve component cleaning will suffice is absurd ! Hi 300' :)

Andre , a word of further caution , rather than waiting to see if it happens again , check your oil level . Any higher than normal level or smell of gasoline will indicate that this may need immediate action , to avoid engine damage . If no gas smell within oil you should be fine , however always shut off fuel valve once done cutting , inlet needle valve can leak by at the most inconvenient time . Good luck with resolution of this issue Bud !

Well guys...I did nothing so far. She said it has run without incident...so far....lol

I’ve had the same problem about every years with my Honda 5-6 year old. Its very frustrating especially when everybody said buy a Honda, I guess this was a dud/kemon year. Though i did have good results replacing the little thermal wax assembly piece behind the carb and my problem was solved twice but now here we go again and I’m sick and tired of the ongoing problems. Maybe its time for an Ego mower!😎