The MoI of two or more things just add about the same axis.
MoI of Shell about CoM axis = 2/3 mr2
MoI of water about CoM axis = 2/5 mr2
Using parallel axis theorem MoI about axis = MoI about CoM + Md2
MoI about given axis = 2/3 mr2 + 2/5 mr2 + 2m r2
ans!!