jmc

We don't know $s(x)$, so we don't have an expression we can simply stick $1$ in to get an answer. We do, however, know that $s(t(x))=x^2+3x-2$. So, if we can figure out what to put into $t(x)$ such that $1$ is output, we can use our expression for $s(t(x))$ to find $s(1)$.

If $t(x)=1$, then $3x-8=1$, which gives $x=3$, so $t(3)=1$. Therefore, we have $s(t(3))=s(1)$. But we also know that $s(t(x))=x^2+3x-2$, so $s(t(3))=3^2+3(3)-2=\boxed{16}$.