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 : Tmb + Fb = Wtmb
The force exerted by water is the Bouyant Force Fb.
Fb = 10N - 8N = 2N
Fb = Vimmersed x g x dwater
2 N = Vimmersed x 9.8N/Kg x 1Kg/L
Vimmersed = 0.2 L
Since the mettalic block is totally immersed, we can conclude Vimmersed = Vtotal , that is the total volume of the metallic block.
Wtmb = dmb x g x VT
10 N = dmb x 9.8 N/Kg x 0.2 L
dmb = 5.1 Kg/L