Potential difference across the $ 4\: ohm$ resistor is zero $ \Rightarrow$ potential difference across
$2\: ohm $ resistor is $4V$ and across $R$ will $-2V$.
The current through the 2 ohm resistor is 2A.
The KVL equation for the big loop is
10 - 2i -iR - 4 = 0
On solving the $KVL$ equations, we get $ R = 1 \: ohm$.
Ans : (A)