a. here, there are no restrictions on where letters can go, so you start with:

xxxxxxxx

there are 8 slots for the first letter, 7 for the second, and so on, so it's 8! (factorial)

b. Mxxxxxxx

there are 7 slots for the first letter, 6 for the second, etc. --> 7!

c. MxTxHxNx

same exact idea as a. and b., but you start with 4 slots

d. xxxxxxNG

starting with 6 slots.....