6. When $s$ and $t$ take all real values, then
$$
(s+5-3|\cos t|)^{2}+(s-2|\sin t|)^{2}
$$

can achieve the minimum value of $\qquad$
6. Consider the line $\left\{\begin{array}{l}x=s+5 \\ y=s\end{array}\right.$ and the elliptical arc
$$
\left\{\begin{array}{l}
x=3|\cos t|, \\
y=2|\sin t|
\end{array}\right.
$$
(as shown in the figure), then the expression represents the square of the distance between any point on the line and any point on the elliptical arc. Clearly, the perpendicular distance from point $A$ to the line is the shortest, i.e., the square of the distance from the point $(3,0)$ to the line is the smallest, which is 2.