Tom ate 1/4 of a pizza. he divided the leftover pizza into pieces each equal to 1/12 of the original pizza. after he gave some friends one piece each 1/6 of the original pizza remained. how many friends got pizza?

To make this easy let covert everything using a LCD.

The LCD of 1/4  1/12 and 1/6  is 12. This becomes...

Tom ate 3/12 of the pizza.
Leftover pizza = 9/12.
Slices were 1/12.
X friends got pizza.
Remaining pizza is 2/12.

if each friend got 1 piece(1/12)
9/12(Leftovers) - 2/12(remaining)  = 7/12

So 7 friends got pizza.