Iknow the answer but i don't know how the book got it.

question:
a teacher accompanied her students on a trip to the museum. she wanted to be certain that she kept track of all the students during the trip, so she counted the students by the color of the coats they were wearing. one-half of the students wore black coats, one-sixth wore red, one-fourth wore blue, and the remaining two students wore green. how many students went on the trip?


t=total # of students
1/2t+1/6t+1/4t+2=t
i know how to convert common denominator so
6/12t+2/12t+3/12t+2=t
but how did they get:
2=1/12t
t=24