To attempt to solve this, I used the radius of the right cylinder created by the line from the interval 0 to 6 and subtracted the volume created by y = $\sqrt{x-2}$. The radius of the right cylinder is πr^2h with radius 2+2=4 and height 6. The volume given by the other function should be:
π $\int_2^6 (\sqrt{x-2}+2)^2 dx $= $136π\over3$
Then my volume = 96π - $136π\over3$ = 159.174, but the answer is 134.04. Where did I make a mistake? Thanks.
Your derivation seems to be correct if the volume is referred to the interval $x\in[0,6]$.