How does this opamp full-wave rectifier work?
Though not ideal it is a full wave rectifier.

For a negative input it is inverted by the op-amp thus becomes a positive output of the opposite polarity, passing through the diode. R1 and R2 set the gain at -1 so a negative input (compared to ground) becomes a positive value at the output.

For a positive input it is inverted but the diode will not let a negative value pass, thus disabling the op-amp and R1 + R2 become bypass resistors so a positive value appears at the outputs, but with 2K of resistance as they have no buffer. If the load is very light or buffered it will behave more like an ideal FW rectifier.

For a true full wave rectifier you need 2 op-amps and 2 diodes, so each polarity can be buffered.