(i) When `V_(A) gt V_(B)` the diode is forward biased. Hence, the resistance of diode will be taken as zero. So the equivalent resistance is
`=(4xx12)/(4+12) Omega=3 Omega`
(ii) When `V_(A) lt V_(B)`, the diode is reverse biased. Hence, there will be no current in the diode branch. So, the equivalent resistance is `12 Omega`