Using Linearity, how can I find Vo in this circuit? (not homework)
Working resistance values from right to left to simplify the circuit.

Series R7 and R8 gives 6k

This value, in parallel with R6, this gives 3k

This value, in series with R5, gives 6k

This value in parallel with R4, gives 4k

This value,in series with R2, gives 8k

This value , in parallel with R3, gives 4k (which is equal to R1) so the voltage at this node (after R1) = 10V

R4,5,6,7 and 8 produce an effective 4k resistance so the voltage at the second node  (after R2) must be be half that value i.e. 10 * 0.5 = 5V.

The voltage across R5 is 5/2V (as R6 // (R7 and R8) = 3K)

So the voltage across R7 and R8 must also  be 5/2V  (= 5 - 5/2).

So Vo = R8/(R7 + R8) * 5/2 =  4/6 * 5/2 = 20/12 or 5/3V