Answer
$y_{com} = -2.0~cm$
Work Step by Step
We can find the y-coordinate of the center off mass:
$y_{com} = \frac{(6L^2)(1.5L)+(4L^2)(2.5L)+(8L^2)(-2L)+(4L^2)(-3L)}{6L^2+4L^2+8L^2+4L^2}$
$y_{com} = \frac{(9L^3)+(10L^3)-(16L^3)-(12L^3)}{22L^2}$
$y_{com} = \frac{-9L^3}{22L^2}$
$y_{com} = -\frac{9L}{22}$
$y_{com} = -\frac{(9)(5.0~cm)}{22}$
$y_{com} = -2.0~cm$
