Question 668552
Start with your two possibilities {H,T}

From each node in your tree sprout another two branches {H,T} until you've done this process 4 times. As a check, you should have 16 end possibilities. As 2^4 = 16.

Then, find the paths in your tree such that T only appears twice. You should get (from top to bottom:

{HHTT}
{HTHT}
{HTTH}
{THHT}
{THTH}
{TTHH}

6 possibilities.

This makes sense because if we have 4 slots to choose from and we need 2 to be tails, there are exactly (4 choose 2) =  4!/2!*2! = 24/4 = 6 ways to do that.