More pictures to see other side

The washout is due to the downspout next to a gate where the grass was probably already stressed from traffic. I can't see that the other downspouts are causing the same problem. I can see that the excess water near the gate wants to run towards the front (?) yard. The easiest fix for this area is to place pavers with gravel between them. It would prevent a muddy walkway while allowing the water to drain away naturally.

The more extreme fix is to put in a French drain or a regular drain pipe connecting directly to the downspouts. Draining this area requires some other area for the water to exit, which could mean putting in 1 or 2 dry wells.

The pavers and gravel would be quick and inexpensive. The drain and dry well would take longer, be expensive and disrupt your existing landscape during construction. Either way, a landscape contractor should be able to do these jobs.

Thank you so much for the help. I’ll be contacting a landscape contractor to do the job.