My thought process:
There are $\frac{12!}{2!2!}$ possible ways of arranging FOO_FIGHTERS total, then I should subtract the number of ways it can be arranged with the underscore on either end.
I believe the possible arrangements of FOO_FIGHTERS with the underscore on the left end would be $\frac{11!}{2!2!}$, then I would multiply that value by two to accommodate for the underscore being on the right end. However, I'm not sure that $\frac{11!}{2!2!}$ is the correct method, because wouldn't that be disregarding the location of the underscore to begin with, or is it irrelevant anyway because it will always be in the same spot?
Edit: Formatted properly with MathJax
Yes, that's correct and the final result is $$\frac{12!}{2!2!}-2\cdot \frac{11!}{2!2!}.$$ The same can be done by multiplying the number of positions of the underscore, i.e. $12-2=10$ ways, by the number of arrangements of the word FOOFIGHTERS: $$10\cdot \frac{11!}{2!2!}.$$