The method for "solving" this involves making assumptions and then calculating an answer. The assumptions could be wrong, which isn't as important, and the interviewer will likely help guide your assumptions if they felt it was necessary. The assumptions here would be about the approximate size of a tennis ball, the approximate volume of the room, etc. Getting fancy, you might begin discussing how the weight of the tennis balls would begin compressing the lower levels, giving more potential room at the top, as well as how the second level of tennis balls would rest in a lattice structure on the first level, sitting in the gaps, and thus not being as high as simply multiplying the diameter of the tennis ball by 2 to get the height of two layers.

There is no correct answer to this question. It's all based on your problem solving abilities.