For the output of the load it does not matter whether you write "+6V" and "GND" near the terminals, or "GND" and "-6V" They're just pencil scratches.
What does matter is where the power supply from the opamp comes from, and how you generate the reference voltage.
Stop working with those numbers for the voltages, and take a closer look at what the circuit is actually doing.
The opamp is just comparing the voltage differential on it's input terminals, and from that it either increases or decreases it's output voltage.
Without showing how the reference voltage on the other opamp terminal is made, there is not much useful that can be said about this partial circuit.
The circuit below is from a simple load I coughed up some years ago, and I designed it to work without a power supply and a reasonably low output voltage.
How it works:
U101A generates a reference voltage of around 1.2V, which is is twice the voltage over the diode. (Because of R103 and R102)
Then the potentiometer makes the reference voltage asjustable, and opamp U101B compares the adjusted reference voltage with the voltage over power resistor R107.
By using Shziklay pair for the amplification between the opamp and the big current sink terminal the power supply voltage can be kept low.
The whole circuit only has 2 external connections, and can be used as either a current sink or current source.
Because the power supply for the opamps are taken from the same 2 terminals, there is a minimum voltage (Just below 3V) and minimum current (around 20mA) for this circuit.
The use of the transistors and opamp is not critical.
LM358 is a quite nice choice because it works from a low power supply voltage and it's input terminals work upto the V- rails.
The transistors on the output are just what I had in the parts bucket.
I did have to tweak it a bit to get it stable. So you will have to add some capacitors too.