Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of height of 5 students (A=162, N=5)

⇒S=162 X 5 =810

Later, height of the 6 th student is included, the average increases by 1 cm. (so A=163, N=6)

So, sum of height if 6 students

⇒S=163 X 6 =978

Now,

The height of 6th student =(sum of height of 5 students)-(Sum of height of 6 students)

=978-810

=168

Hence, Option D is correct.