We know that they have:
2 entrences
3 ways to choseĀ (escalator,elevator and stairs)
8 gates
and again 3 ways to chose (escalator, elevator and stairway)
now you have to multiply it:
\(2*3*8*3=6*8*3=48*3=144\)
There are 144 different ways that Anita and Terry can go from street level to the trains:)