Showing that there exists an algorithm, that converts NFA to DFA under some cirumstances
The main idea is that if the NFA has at most 10 runs over each word, then when reading a word, at any given point the NFA can be in at most 10 states. Therefore in the powerset construction it suffices to consider sets of at most 10 states, of which there are polynomially many.

All remaining details are left to you.