When two identical cells are connected either in series or in parallel across a 4 ohm resistor, they send the same current through it. The internal resistance of the cell in ohm is

Let voltage of each cell is  = E, 

internal resistance of each cell is  = r

When cells are in series :

 Effective voltage of circuit = E + E = 2E

And effective resistance of circuit = r + r + 2 = 2(1 + r)

Current $I_1 =\frac{E}{ (1+r)}$

When cells are in parallel :

Effective voltage of circuit = E  

Effective resistance of circuit = $=\frac{ r}{2}+2=\frac{r+4}{2}$

Current $I_2=\frac{2E}{r+4}$

As $I_1=I_2$

$⟹ \frac{E}{(1+r)}=\frac{2E}{(r+4)}⟹r=2\Omega$