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The percentage of the volume occupied in...

The percentage of the volume occupied in three dimensional space for the simple cubic, bcc and fcc lattices respectively will be:

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The arrangement of atoms in hcp is of ABABAB … type and in case of fcc is of ABCABCABC … type. Both in hcp and fcc, the layers are formed of same atoms in similar arrangements but the only difference is the placement of layers on top of each other. Hence, both have same packing fraction. In both the arrangements, the number of atom of same size present around the atom is maximum, i.e. 6. So, the packing fraction is highest.
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