Answer
$19$
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 $\mathbf a= \langle 4,1,\frac{1}{4} \rangle$ and $\mathbf b= \langle 6,-3,-8 \rangle$, $$\mathbf a \cdot \mathbf b =4(6)+1(-3)+\frac{1}{4}(-8)=24-3-2=24-5=19.$$