We need to evaluate $f_{\Theta \vert X}(\theta \vert x)$ in order to get $E[\Theta \vert X]$.

$f_{X,\Theta}(x,\theta) = f_{X}(x) f_{\Theta \vert X}(\theta \vert x)$ which is a parallelogram on the $\theta-x$ plane at the points $(3,4)$, $(5,4)$, $(9,10)$ and $(11,10)$. Then $E[\Theta \vert X]$ can be obtained by drawing vertical lines on the planes and calculating the $E[\theta]$ over that line. It is a line which bends at two points.