The lines [tex]y=\frac x2[/tex] and [tex]y=3-x[/tex] meet when
[tex]\dfrac x2 = 3-x \implies \dfrac{3x}2 = 3 \implies x=2[/tex]
at which point [tex]y=\frac22 = 1[/tex]. They also have [tex]y[/tex]-intercepts of [tex]y=0[/tex] and [tex]y=3[/tex], respectively.
Split the region up at [tex]y=1[/tex]. Then the integral of [tex]f[/tex] in the opposite order of variables is
[tex]\displaystyle \int_0^1 \int_0^{2y} f(x,y) \, dx \, dy + \int_1^3 \int_0^{3-y} f(x,y) \, dx \, dy[/tex]
