Interesting question! Let's first break this up:
[tex] \frac{4!8!}{2!7!}= \frac{1x2x3x4x1x2x3x4x5x6x7x8}{1x2x1x2x3x4x5x6x7} [/tex]
We can now simplify this by crossing out numbers that appear in both denominator and numerator. This becomes
[tex] \frac{3x4}{1} [/tex]
Therefore, the answer is 12
