6. Let the base edge length and height of the regular quadrilateral pyramid $P-ABCD$ be equal, and let point $G$ be the centroid of the side face $\triangle PBC$. Then, the sine value of the angle formed by line $AG$ and the base $ABCD$ is $\qquad$ .
Given that $A B=P O=6$, then
$$
\begin{array}{l}
G H=\frac{1}{3} P O=2, H M=\frac{1}{3} O M=1, M B=3 \\
\Rightarrow A H=\sqrt{5^{2}+3^{2}}=\sqrt{34}, \\
\text { thus } \tan \angle G A H=\frac{2}{\sqrt{34}} \\
\Rightarrow \sin \angle G A H=\frac{2}{\sqrt{38}}=\frac{\sqrt{38}}{19} .
\end{array}
$$