More info please. Is the pic your neighbor’s house? Don’t see a gutter along the roof line or corner down spouts. Any chats with them about plans to replace gutters & telling them about water damage to your yard? In most cities there’s code about surface water management of water runoff created from one’s property - that is, not allowed to drain off onto another neigboring property.

Yes neighbora house and no llans to replace gutter

Where’s property line between your yard & neighbor’s in this picture?

Can you provide photos of the "destroyed" plants and lawn? Nothing looks too bad based on what you have provided.

It would also be helpful to know where geographically you are located (not growing zone!!) and the distance from your neighbors' eaves or missing gutters and where you perceive any damage to be. If it is more than a few feet, the lack of gutters is not to blame

The property line is at ther house.

the plants is not the issue, its what can i out there so the water doesnt puddle there. it washes the mulch away so i was thinking gravel?

Or actually hearty water olants could do the trick. i live in south florida, fort lauder area