Answer
$-1$
Work Step by Step
The dot product of two vectors $\mathbf a= \langle a_1,a_2,a_3 \rangle$ and $\mathbf b= \langle b_1,b_2,b_3 \rangle$ is $a_1b_1+a_2b_2+a_3b_3$.
So for $\mathbf a= \langle 6,-2,3 \rangle$ and $\mathbf b= \langle 2,5,-1 \rangle$, $$\mathbf a \cdot \mathbf b =6(2)+(-2)(5)+3(-1)=12-10-3=2-3=-1.$$