Label the lengths of the vertical and horizontal segments as $a, b, c, d$. Rectangle W is $b$ by $c$, so its perimeter is $2 b+2 c$, which equals 2. Rectangle X is $b$ by $d$, so its perimeter is $2 b+2 d$, which equals 3. Rectangle Y is $a$ by $c$, so its perimeter is $2 a+2 c$, which equals 5. Rectangle Z is $a$ by $d$, so its perimeter is $2 a+2 d$. Therefore, $2 a+2 d=(2 a+2 b+2 c+2 d)-(2 b+2 c)=(2 a+2 c)+(2 b+2 d)-(2 b+2 c)=5+3-2=6$.