Huffy 24 Alpine mountain bike POWER shifter compatibility
A 24 gear bike means you have 8 sprockets in the rear and 3 on the crank. Any shifters for 3 front gears and 8 rear will work, that match the manufacturers of the derailleurs. 

If derailleurs are Shimano you need Shimano shifters. If the derailleurs are SRAM you need SRAM shifters.