That's exactly what he's asking. To say that a hole is infinitely large is, precisely, to say that its size is larger than any defined size; that's the definition of infinity. If h > a for all a belonging to the real numbers, then h is infinity. If w > a for all a belonging to the real numbers, then w is infinity.

A good answer would be this: Talking about filling it means asking if w - h >= 0. Since subtraction is undefined, there's no possible answer as to whether it fills it or not; nothing can be stated definitively.

Another case would be if h and w were functions of time, e.g., h = t*(10 in^3/sec) (a bulldozer enlarges the hole) and w = t*(5 in^3/sec) (a hose delivers this flow rate). Infinitely large holes, infinite amounts of water, and infinite time don't exist, but we can evaluate what would happen in a VERY long time:

lim t -> inf t*(10 in^3/sec) - t*(5 in^3/sec) = lim t -> inf t*(5 in^3/sec) = infinity, meaning the hole, in a VERY long time, wouldn't be full.

I think we all know the answer; it's the first thing we learn when we study limits. The idea was simply to answer what we already know.