You have to find a farm with PLANT MONSTERS. The trees and decorative stuff don't count.
When you go to someone's farm, check their monsters at the bottom left of the screen. Check the INFO on each monster and at the top, under it's level bar it tells what KIND of monster it is. Look for monsters that say Plant. When you find one, click "Play" on the Info screen.
You can only click on any specific monster ONE time per day, so if you need to play with 5 plants for the quest, you need to find 5 DIFFERENT kinds of Plants.
You'll probably have to visit dozens of peoples' farms before you can find enough Plants to complete the quest.
Also, Mushrooms do NOT count as Plants, they count as Mushrooms.