It doesn't matter how tall the building is as long as it is tall enough for the
elevator to drop 120 feet.  It also doesn't matter how many floors it has.  So
let's suppose the building has 100 floors and that the elevator stops at each
floor.

When the elevator has dropped 12.3 feet and stops at the 99th floor you have
passed 1 floor, the 99th one, from the bottom of the 100th floor, where your
feet were at the start, to the bottom of the 99th floor.

When the elevator has dropped another 12.3 feet and stops at the 98th floor you
have dropped 24.6 feet and passed 2 floors.

When the elevator has dropped another 12.3 feet and stops at the 97th floor you
have dropped 36.9 feet and passed 3 floors.

When the elevator has dropped another 12.3 feet and stops at the 96th floor you
have dropped 49.2 feet and passed 4 floors.

When the elevator has dropped another 12.3 feet and stops at the 95th floor you
have dropped 61.5 feet and passed 5 floors.

When the elevator has dropped another 12.3 feet and stops at the 94th floor you
have dropped 73.8 feet and passed 6 floors.

When the elevator has dropped another 12.3 feet and stops at the 93th floor you
have dropped 98.4 feet and passed 7 floors.

When the elevator has dropped another 12.3 feet and stops at the 92th floor you
have dropped 110.7 feet and passed 8 floors.

Since the elevator drops only 120 feet, it won't make it to the 91st floor, for
that would be a drop of 123.0 feet. So since it only drops 120 feet it will be
3 feet above the 91st floor, and your feet will have passed 8 floors plus
12.3-3 or 9.3 feet which is 9.3/12.3 or 31/41sts of another floor.

Answer: You will have passed 8 31/41 floors.

Note: I predict your teacher will disagree with this answer.  But if so, then
he or she is wrong, for it is the only correct one.

Edwin