Question

____ tired, he managed to finish it on time.

Though
Despite
Either could be used here.

Answer 1

despite

Step-by-step explanation:

despite he was tired, he managed to finish it on time.

Answer 2

_Though_ tired, he managed to finish it on time.

Step-by-step explanation:

though it would make more sense and despite wouldn't. Either could be used here would be false because you can have a word in the sentence like though so answer is though.