Approaching the job of shifting an entire mountain

How would you go about moving a well-known mountain to a different location?

Clarify the goal, then estimate the scale and the logistics. Ask where it must go and why. Approximate the mountain as a cone (a peak about $3.7$ km high with a $20$ km base radius has volume $\tfrac13\pi r^2h\approx1500\ \text{km}^3$), then divide by what a truck, train or conveyor can move per day to estimate the effort, which runs to many thousands of years with conventional equipment. The interviewer is testing structured thinking, not geology.