Step 1:

It is stated that the mean=6 and the standard deviation =3

$\therefore np=6$

$\sqrt{npq}=3$

$npq=9$

Step 2:

From the above $\large\frac{npq}{np}=\frac{9}{6}=\frac{3}{2}$

$\Rightarrow q=\large\frac{3}{2}$ which is not possible

Since $0 < q < 1$

$\therefore$ the statement is false.