Let f be a real valued function defined as $\mathrm{f}:\mathrm{R}\to \mathrm{R}, \mathrm{f}\left(\mathrm{x}\right)=|{\mathrm{x}}^2-6\mathrm{x}+8|\sin \left((\mathrm{x}-2)\mathrm{\pi }\right)+|{\mathrm{e}}^{\mathrm{x}}-1|\mathrm{sinx}+\left|{\mathrm{x}}^2\right|$
The number of points of non-differentiability is

$|{\mathrm{x}}^6-6\mathrm{x}+8|$is non differentiable at x = 2, 4
at x = 2, 
at x = 2, $\sin \left((\mathrm{x}-2)\mathrm{\pi }\right)=0$
$\mathrm{x}=4\sin \left((\mathrm{x}-2)\mathrm{\pi }\right)=0$
So $|{\mathrm{x}}^2-6\mathrm{x}+8|\hspace{0.17em}\hspace{0.17em}\sin \left((\mathrm{x}-2)\mathrm{\pi }\right)$ is differentiable everywhere
Similarly, $|{\mathrm{e}}^{\mathrm{x}}-1|\mathrm{sinx}$ is differentiable every where and $\left|{\mathrm{x}}^2\right|$ is differentiable is differentiable