6. When $s$ and $t$ take all real values, the minimum value that $(s+5-3|\cos t|)^{2}+(s-2|\sin t|)^{2}$ can achieve is
2
6.【Analysis and Solution】Consider the line $\left\{\begin{array}{l}x=s+5 \\ y=s\end{array}\right.$ and the ellipse arc $\left\{\begin{array}{l}x=3|\cos t| \\ y=2|\sin t|\end{array}\right.$ (as shown in the figure), then the original expression represents the square of the distance between any point on the line and any point on the ellipse 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.