During the first half cycle of input
V = 4 Volts makes the diode in the Forward biased condition so the equivalent circuit will be as per Fig. - 1 and the output voltage will be +4 Volts till the input reaches at 4 Volts.
When the input rises beyond the 4 Volts (From 4 to 16 Volts and after reaching at peak reduces from 16 to 4 volts), the diode comes in the reverse biased condition. Hence the output follows the input as shown in Fig. - 2 .
When the supply voltage falls below the 4 Volts then D comes in forward bias from the 4 V battery supply. Therefore, output will be 4 Volts for the rest of the cycle as shown in Fig. - 3 .