If it takes (a) men (b) hours to dig (c) holes, how many men are required to dig b holes in c hours?
give answer in terms of a, b,c

Well, let's see . . .

You said that  (a) men can dig (c) holes in (b) hours.

So . . . It takes  (a) men  (b / c) hours to dig one hole.

And . . . It takes    One man  (a b / c) hours to dig one hole.

Now . . .  There are  (b) holes to be dug.

              It would take one man  (a b / c)·(b) = (a b² / c) hours to dig them all.

              But if you had 'x' men, it would only take them  (c) hours to do it.

So          c  =  (a b² / c)  /  x

           x c  =  (a b² / c)

           x     =  a b² / c²  men   . 

Now, I lost the big overview while I was doing that,
and just started following my nose through the fog.
So I have to admit that I'm not that confident in the answer.
But gosh durn it.  That's the answer I got, and I'm stickin to it.
Rrarrup !