Learn Finnish: Sinun täytyy leikata vanhat pensaat.

This is the plural total object! When a plural object is involved in a complete action, it takes the -t ending. Since you must cut all of these specific bushes, they act as a total object. Notice that the adjective (vanhat) has to match the noun (pensaat) and also gets the -t ending.

Why is the word for 'you' in the genitive form (sinun) instead of just sinä?

This is because of the verb täytyy (must / have to). Sentences expressing necessity always require the subject (the person who has to do something) to be in the genitive case, which ends in -n.

Wait, I learned that objects in täytyy sentences don't take special object endings. Does that apply here?

You are remembering correctly for singular objects! If you were cutting just one bush, the object would be in the basic dictionary form instead of having its usual -n object ending (Sinun täytyy leikata vanha pensas). But for plural objects, the rule is different: plural total objects always keep their -t ending, even in necessity sentences like this one.

How does the dictionary form pensas turn into pensaat?