Here given that

density of a material in SI units is 128 kg m^–3

And a new unit system is introduced where 1 unit of length = 25 cm and 1 unit of mass = 50 g

You should know that, physical quantity is same in any unit system. And to calculate a physical quantity yo should know two things

(1) numerical value of the physical quantity (n)

(2) unit of the physical quantity (u)

And n $$ \times $$ u = constant in any unit system.

Here in SI unit system,

n₁ = 128

u₁ = kg/m³

And in new unit system,

n₂ = ?

u₂ = 50gm/(25cm)³

As n₁u₁ = n₂u₂

$$ \therefore $$ 128 $$ \times $$ (kg/m³) = n₂ $$ \times $$ 50gm/(25cm)³

$$ \Rightarrow $$ 128 $$ \times $$ $${{1000\,gm} \over {{{\left( {100\,cm} \right)}^3}}}$$ = n₂ $$ \times $$ $${{50\,gm} \over {{{\left( {25\,cm} \right)}^3}}}$$

$$ \Rightarrow $$ n₂ = 128 $$ \times $$ $${{20} \over {{4^3}}}$$ = 40