Take the task of distributing the 4 different balls and break it into stages.

Stage 1: Select a box for the 1st ball to go into.
There are 3 available boxes, so we can complete stage 1 in 3 ways

Stage 2: Select a box for the 2nd ball to go into.
There are 3 available boxes, so we can complete stage 2 in 3 ways

Stage 3: Select a box for the 3rd ball to go into.
There are 3 available boxes, so we can complete stage 3 in 3 ways

Stage 4: Select a box for the 4th ball to go into.
There are 3 available boxes, so we can complete stage 4 in 3 ways

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus distribute all 4 balls) in (3)(3)(3)(3)(4) ways (= 81 ways)

Answer: B