Micro-economics exercise (I need help please)

Hello :-)

The lecturer gave us an exercise and I don't understand how to solve it, I would appreciate help please.

The exercise:

Show that weak transitivity implies strong transitivity. (Hint. Show if z ≥ x, then there is a contradition in that z ≥ y).

I know that weak transitivity means that if x ≥ y and y ≥ z then x ≥ z, and that strong transitivity means if x > y and y > z then x > z, but I can't understand the connection between this and that hint in the exercise, I'm really confused.

Thank you!