This question requires high level description of Turing machine.
I found that we are able to solve a^n b^m c^nm by :
Step 1 : crossing out one a
Step 2 : continue to cross out one b followed by one c once until b are all crossed out.
Step 3 : we restore all the b's and continue looping until all a's are crossed out.
If there is no c left, we accept. Else, reject.
I was thinking if this would be related to the question where c has a power of ( 2 ^nm )?