The value of n so that vectors  $\mathrm{A}=4\widehat{\mathrm{i}}+\mathrm{n}\widehat{\mathrm{j}}-\widehat{\mathrm{k}}\text{ and }\mathrm{B}=2\widehat{\mathrm{i}}+3\widehat{\mathrm{j}}+2\widehat{\mathrm{k}}$are perpendicular to each other is 

A and B will be perpendicular to each other if A. B = 0.
i.e $(4\widehat{\mathrm{i}}+\mathrm{n}\widehat{\mathrm{j}}-\widehat{\mathrm{k}})\cdot (2\widehat{\mathrm{i}}+3\widehat{\mathrm{j}}+2\widehat{\mathrm{k}})=0\Rightarrow 8+3\mathrm{n}-2=0\Rightarrow \mathrm{n}=-2$