The number of integers greater than 6000 that can be formed, using the digits 3 ,   5 ,   6 ,…

$4$ digit and $5$ digit numbers are possible.

$4$ digit numbers:

$\begin{array}{cccc}6/7/8& & & \\ \overline{\uparrow }& \overline{\uparrow }& \overline{\uparrow }& \overline{\uparrow }\\ 3& 4& 3& 2\end{array} Total\; numbers\; possible=\text{3 . 4 . 3 . 2}=\text{72}$

$5$ digit numbers

$\begin{array}{ccccc}\overline{\uparrow }& \overline{\uparrow }& \overline{\uparrow }& \overline{\uparrow }& \overline{\uparrow }\\ 5& 4& 3& 2& 1\end{array} Total\; numbers\; possible=\text{5 . 4 . 3 . 2 . 1}=\text{120}$

$\therefore \text{Total numbers}=72+120=192$