Given, mass of disc, $M=4 \mathrm{~kg}$
Radius of disc, $R=0.4 \mathrm{~m}$
Initial angular velocity of disc, $\omega_1=30 \mathrm{rad} \mathrm{s}^{-1}$
Mass of point-masses, $m=0.25 \mathrm{~kg}$
Now, moment of inertia of disc, $I_1=\frac{1}{2} M R^2$
Moment of inertia of disc and two point mass system,
$I_2=\frac{1}{2} M R^2+2 m R^2$
Let $\omega_2$ be the final angular velocity.
According to conservation of angular momentum,
$I_1 \omega_1=I_2 \omega_2 \Rightarrow \omega_2=I_1 \omega_1 / I_2$
Substituting the values, we get
$\omega_2=\frac{\frac{1}{2} M R^2(30)}{\left(\frac{1}{2} M R^2+2 m R^2\right)}$
$=\frac{\frac{1}{2} \times 4 \times(0.4)^2 \times 30}{\frac{1}{2} \times 4 \times(0.4)^2+2 \times 0.25 \times(0.4)^2}$
$\omega_2=24 \mathrm{rad} / \mathrm{s}$
Hence, the final angular velocity of system is $24 \mathrm{rad} / \mathrm{s}$.