Answer is: 4.826 grams of anhydrous nickel(II) sulfate could be obtained.
m(NiSO₄×7H₂O) = 8.753 g; mass of heptahydrate.
m(NiSO₄×6H₂O) = 8.192 g; mass of hexahydrate.
m(H₂O) = m(NiSO₄×7H₂O) - m(NiSO₄×6H₂O).
m(H₂O) = 8.753 g - 8.192 g.
m(H₂O) = 0.561 g.
m(NiSO₄) = m(NiSO₄×7H₂O) - 7 · m(H₂O).
m(NiSO₄) = 8.753 g - 7 · 0.561 g.
m(NiSO₄) = 4.826 g.