We have,

a = 0.27nm = $0.27 \times 10^{-9}$ m.

A = 65.37

As Zn has HCP structure,

we know, 

$3 \sqrt{2} a^{3} \rho = n \dfrac{M}{N} $

where M= Atomic weight of Zn, N= Avagadro's number= 6.023 \times 10^{23} 

Mass=$ n \dfrac{A}{N}$

$=6 \times \dfrac{65.37}{6.023 \times 10^{26}}$

$=6.512 \times 10^{-25}$ kg.

Volume of unit cell= $3 \sqrt{2} a^{3}$

= $3 \sqrt{2} \times (0.27 \times 10^{-9}) ^{3}$

= $8.3508 \times 10^{-29}$ m3

Density=$\dfrac{Mass}{Volume} $

= 7798.0553 kg/m3

Atomic packing factor of a HCP unit cell = $\dfrac{\pi}{3 \sqrt{2}}$ = 0.74.