Period of $|\cos x| = \pi$ And period of $\sin x = 2\pi$ Graph of $\sin x$ and $|\cos x|$ cuts each other at two points A and B in $\left[ {0,2\pi } \right]$ So, in $\left[ { - 4\pi ,4\pi } \right]$, total 4 similar graph will be present and graph of $\sin x$ and $|\cos x|$ will cut $4 \times 2 = 8$ times. $\therefore$ Total possible solutions = 8.