In geometry questions the absence of graphs makes the solution difficult to see. So try to develop the habit making a quick sketch.

So if you have point A (dressing room 1) and point B (dressing room 2) with the distance between them 16f and a point X (cash register) on equal distance between them; therefore, that makes the minimum distance of 8f. Also, the trick here is to realize that point X does not necessarily lays on the line AB but could form an isosceles triangle with any distance between point A and B (as long AX and BX are equal)

Answers II and III are correct.

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Try and fail, but don't fail to try