Write a triple integral, including limits of integration, that gives the volume between $2x+3y+z = 8$ and $3x+6y+z = 8$ and above $x+y\le 2, x\ge 0, y\ge 0$.

volume = $\int_a^b\int_c^d\int_e^f$ $d$ $d$ $d$
where $a =$ , $b =$ ,
$c =$ , $d =$ ,
$e =$ , and $f =$ .
(Note: values for all answer blanks must be supplied for this problem to be able to check the answers provided.)