At the end of 40 hours, 6.25% of the original radionuclide is present in a sample. what is the half-life of the radionuclide?

Work backwards. double the percentage until it reaches 100%. how many times did you have to double it? divide 40 by the number of times you had to double it.
like so:
6.> 12.> > > 100
so you doubled it 4 times, then divide 40/4= 10 hours. so half life is 10 hrs.