Consider all possible values of R in circuit shown. Then the maximum possible rate at which energy can be supplied by the ideal battery to the given combination of resistors is equal to

So here we want power delivered by battery should be maximum

Power delivered by battery (V) to a resistance (R)

$\mathrm{P}=\frac{{\mathrm{V}}^2}{\mathrm{R}}$

So, for a given battery if R is minimum then P is maximum
So, here

If R = 0 then equivalent resistance of circuit is minimum so $10 \Omega$

It would be short circuited So equivalent resistance of circuit

${\mathrm{R}}_{eq}=20\mathrm{\Omega }$

$\mathrm{P}=\frac{(20{)}^2}{\left(20\right)}=20\mathrm{W}$