The needle also fell out. Which end of the needle goes where? Thanks again for the help.

It can really only go 1 way. The tip on the float valve goes into the chamber against the seat.The float will be close to parallel to the body of carb when the bowl is full of fuel.

My Toro 20016 SN 2204004861 has this Honda OHC 5.5 on it. The engine number on the Honda engine is GJAE 1516487 A1A. The carb number is BB62BDNA11. The controls from the mower has 3 wire controls leading to the carb. One small wire that - I think - connects to the small hole on the spindle on the right side(standing at the back of the mower) of the carb (opposite side from the black spindle)
There are two other larger wires (one longer than the other) that I'm not sure where they go. On the black - left - side probably. There are two larger holes on the black spindle. With all numbers described above, if I was to replace the carb with a new one, any idea on what the part number would be?
Thanks again very much.