Anhydrous means compound without water content,
so first we want to find out how much water evaporated

         5.125 g (whole compound)
- 2.797 g (grams CoCl₂) /          2.328 g (H₂O evaporated)

now we want to convert both water and cobalt(II) chloride to moles

2.797 g CoCl₂

1 mole CoCl₂ / 129.83 g CoCl₂

= 0.02154 moles CoCl₂

2.328 g H₂O

1 mole H₂O / 18.02 g H₂O

= 0.129 moles H₂O

a mole to mole ratio shows

0.129 moles H₂O / 0.02154 moles CoCl₂

= 5.99

for every 1 mole of CoCl₂ there are 6 moles of H₂O

hence, the value of n = 6

CoCl₂ * 6 H₂O