Vectors $-3\hat{\mathrm{i}}+4\hat{\mathrm{j}}+\mathrm{\lambda }\hat{\mathrm{k}}$ and $\mathrm{\mu }\hat{\mathrm{i}}+8\hat{\mathrm{j}}+6\hat{\mathrm{k}}$ are collinear, 

Then,$\left(-3\hat{\mathrm{i}}+4\hat{\mathrm{j}}+\mathrm{\lambda }\hat{\mathrm{k}}\right)\times \left(\mathrm{\mu }\hat{\mathrm{i}}+8\hat{\mathrm{j}}+6\hat{\mathrm{k}}\right)=\left|\begin{array}{ccc}\hat{\mathrm{i}}& \hat{\mathrm{j}}& \hat{\mathrm{k}}\\ -3& 4& \mathrm{\lambda }\\ \mathrm{\mu }& 8& 6\end{array}\right|=0$

$\hat{\mathrm{i}}\left(24-8\mathrm{\lambda }\right)-\hat{\mathrm{j}}\left(-18-\mathrm{\mu \lambda }\right)+\hat{\mathrm{k}}\left(-24-4\mathrm{\mu }\right)=0$

$\Rightarrow 24-8\mathrm{\lambda }=0 \& -24-4\mathrm{\mu }=0$

$\therefore \lambda =3 \& \mu =-6$

$\Rightarrow \lambda -\mu =3+6=9$