$\text{ Let }f\left(x\right)=\left|x-2\right|\text{ and }\underset{\left(n\text{ times }\right)}{\underbrace{g\left(x\right)=f\left(f\right(f\dots \dots \left(f\right(x\left)\right))\dots )}}.\text{ If equation }g\left(x\right)=k, k\in \left(0,2\right)\text{ has }8$ $\text{ distinct solutions than value of }n\text{ is equal to }$

$If n=1 then f\left(x\right) =\left|x-2\right| , number of solutions =2 ;$

$If n=2 then f\left(f\left(x\right)\right)=\left|\left|x-2\right|-2\right| , number of solutions =4 ;$

$If n=3 then f\left(f\left(f\left(x\right)\right)\right)=\left|\left|\left|x-2\right|-2\right|-2\right|, number of solutions =6;$

  $If n=4 then f\left(f\left(f\left(f\right)\right)\right) = \left|\left|\left|\left|x-2\right|-2\right|-2\right|-2\right| ,number of solutions =8;$