This seems like Fluid statics to me.

From Netwon's 2nd law, sum of forces = 0 at Eq

This means Tension = Weight of the mb ( before inserting it in water )

This implies Wt of the mb = 10 N

When inserted in water, I'll assume that the metallic block reaches equilibrium without reaching the buttom surface.

At Eq : T_{mb} + F_{b} = Wt_{mb}

The force exerted by water is the Bouyant Force F_{b}.

F_{b} = 10N - 8N = 2N

F_{b} = V_{immersed} x g x d_{water}

2 N = V_{immersed} x 9.8N/Kg x 1Kg/L

V_{immersed} = 0.2 L

Since the mettalic block is totally immersed, we can conclude V_{immersed} = V_{total} , that is the total volume of the metallic block.

Wt_{mb} = d_{mb} x g x V_{T}

10 N = d_{mb} x 9.8 N/Kg x 0.2 L

d_{mb} = 5.1 Kg/L