Arranging objects with restrictions

There are 6 men and 9 women and they need to be seated in a row of 15 chairs. How many ways are there to arrange them such that the 6 men sit next to each other?

This is what I have done so far. There are 15! ways of arranging the entire group. Arranging the 6 men is 6!. In addition, there is the question of where you place the group of 6 men. It could be

6 men and then 9 women

a woman, 6 men and then 8 women

2 women, 6 men and then 7 women

...

etc

I do not know how to count these possibilities. I know what the answer is (from answer key) but I just can't arrive at it.

Thanks for taking the time to read my question!