Estás en un parque donde muchas personas comen y beben. Mantén limpio el parque. This means you are in a park where lots of people eat and drink. Keep the park clean. It's an imperative expression, meaning you must keep it clean. "Haz tu trabajo" means "do your job", which has no sense in this context. "No vayas al parque" means "don't go to the park" which also has no sense since you already are in the park.
