8. Algebraic expression
$$
\begin{array}{l}
\sqrt{9 x^{2}+4}+\sqrt{9 x^{2}-12 x y+4 y^{2}+1}+ \\
\sqrt{4 y^{2}-16 y+20}
\end{array}
$$

When it reaches the minimum value, the values of $x$ and $y$ are respectively $\qquad$
8. As shown in Figure 4, we have
$$
\begin{array}{c}
\text { Original expression }=\sqrt{[0-(-2)]^{2}+(3 x-0)^{2}}+ \\
\sqrt{(1-0)^{2}+(2 y-3 x)^{2}}+ \\
\sqrt{(3-1)^{2}+(4-2 y)^{2}} \\
=A B+B C+C D \geqslant A D,
\end{array}
$$

where \( A(-2,0) , B(0,3 x) , C(1,2 y) , D(3,4) \), and when points \( B , C \) are on the line segment \( A D \), the original expression reaches its minimum value.
When the original expression reaches its minimum value, we have
\(\frac{3 x}{2}=\frac{4}{5}\), solving for \( x \) gives \( x=\frac{8}{15} \);
\(\frac{2 y}{3}=\frac{4}{5}\), solving for \( y \) gives \( y=\frac{6}{5} \).