Diodes and resistors theory
The voltage drop over R1+D1 and R3 is the same: V1 + 0.6 = V3
The currents through R1 and R3 add up in R2: I1 + I3 = I2
The total voltage drop is 12 V: V3 + V2 = 12
And Ohm's law: 1 kΩ × I1 = V1, 1 kΩ × I2 = V2, 1 kΩ × I3 = V3
These six equtions are enough to compute the results,