Circuit analysis with diode
Remove the diode, you have 2 voltage dividers connected to DC sources. There's 4V over R2, + at NODE1. There's 6V over R4 + at NODE2.

Put the diode back. It has 2V reverse bias, it affects nothing except some  leakage. In datasheet the leakage is 10uA at 1000V reverse voltage. It cannot be more with 2V reverse. The exact leakage can only be estimated with some diode model or measured in a practical circuit.

To stay in truth, this reasoning utilized Thevenin's equivalents of the voltage division circuits. You can continue with them if you assume some leakage current, for ex. just that 10uA or find a better estimate.

If you assume that the leakage through D1 is somewhere between 0 and 10uA, you get the limits for the voltage between NODE1 and NODE2. The upper limit is that 2V assuming the leakage =0.