During a workout, a person repeatedly lifts a 12 lb barbell through a distance of 1.5 ft. How many "reps" of this lift are required to burn off 105 Cal?

I know you use the equation, Q=mgh
m=5.448 kg
height = .4572m

use these conversions instead of above.
its easy to find Q, but what I don't know is how to find how many reps the person shoud do to lose the calories...

You have to convert joules that you got into calories, or calories required into joules required.

Then, divide the required amount by the energy spent on each 'rep'.

I hope it helped! :)