Answer
The person's mass is $28kg$
Work Step by Step
When the person stands at a distance of $R_1=1.5m$ from the center, the total moment of inertia is $$I_1=I_{carousel}+m_{person}R_1^2=125+2.25m$$
When the person stands at a distance of $R_2=0.75m$ from the center, the total moment of inertia is $$I_2=I_{carousel}+m_{person}R_2^2=125+0.56m$$
Angular momentum is conserved, so $$I_1\omega_1=I_2\omega_2$$ $$(125+2.25m)0.6=(125+0.56m)0.8$$ $$75+1.35m=100+0.45m$$ $$0.9m=25$$ $$m=28kg$$
