The transformation is a dilation with a scale factor of 1/3, this means we have to multiply each coordinate with this scale factor to find G'. Let's do it.
[tex]G(3,-6)\rightarrow G^{\prime}(3\cdot\frac{1}{3},-6\cdot\frac{1}{3})\rightarrow G^{\prime}(1,-2)[/tex]We repeat the process for each vertex.
[tex]E(-3,6)\rightarrow E^{\prime}(-3\cdot\frac{1}{3},6\cdot\frac{1}{3})\rightarrow E^{\prime}(-1,2)[/tex][tex]F(3,6)\rightarrow F^{\prime}(3\cdot\frac{1}{3},6\cdot\frac{1}{3})\rightarrow F^{\prime}(1,2)[/tex][tex]H(-3,-6)\rightarrow H^{\prime}(-3\cdot\frac{1}{3},-6\cdot\frac{1}{3})\rightarrow H^{\prime}(-1,-2)[/tex]