ΔU = -Wint
Consdier the work of of interaction is W =m*g*h - equation -1
and the Potential energy U.
Final Potential energy Uf =0 , And the Initial Potential Energy Ui =m*g*h
Now we will write the equation for a Change in Potential energy ΔU,
ΔU = Uf - Ui
= 0-m*g*h
ΔU = -m*g*h --Equation 2
Now compare the both equation
Wint = -ΔU
we can rewrite the above equation
ΔU = -W.
So our Answer is ΔU = -W. .