A radioactive sample contains 10mCi of activity. 8 hours later only 2.5mCi remain. What is the half-life?

The half life is the time a substance takes to become half its original mass, hence, half the activity.

How many times do you have to half 10mCi to get 2.5mCi ?

That many is the number of half lives that occurred.

So many half lives take 8 hours.
Find how much time 1 half life takes, and that is your value of half life.