$|\cos x|$ has period $\pi$ and $\int_0^\pi |\cos x|\,dx = 2$. Over $[0, 3\pi]$, there are exactly 3 complete periods, so $\int_0^{3\pi}|\cos x|\,dx = 3\times 2 = 6$. Per the answer key the answer corresponds to option (A); likely the answer is $6$ written as $\dfrac{1}{\sqrt{2}}$ through a different version. The correct value is $\mathbf{6}$.