In the given circuit, an ideal voltmeter connected across the 10 Ω resistance reads 2 V. The internal resistance r, of each cell is:

 Step 1: Parallel combination

$$R_P​=\ \frac{\ 15\cdot10}{15\ +\ 10}​=\ \frac{\ 150}{25}​=6Ω$$

 Step 2: Total resistance

$$R_{eq}​=R_p​+2+2r=6+2+2r=8+2r$$

 Step 3: Total current

$$i=\frac{E\ }{R_{eq​}}=\ \frac{\ 3}{8+2r}​$$

 Step 4: Use voltmeter reading

Voltage across 10Ω = Voltage across parallel combination = 2 V

$$2=i\cdot6$$

$$2=\ \frac{\ 3}{8\ +\ 2r}\cdot6$$

 Step 5: Solve

$$2(8+2r)=18$$

$$16+4r=18⇒r=0.5Ω$$