Step 1:

Find the current through 6 resistor :

Super Position Theorem :

Take one voltage source at a time and replace all other with short or internal resistance.

Indicate the direction of current in the above circuit.

Equivalent resistance :

9 resistor is in parallel with 6 resistor.

Resistance R_T is in series with 7 resistor.

Step 2:

Circuit current :

Current across each resistor :

Step 3:

Now Short circuit the second voltage source.

Indicate the direction of current in the above circuit.

Equivalent resistance :

7 resistor is in parallel with 6 resistor.

Resistance R_T is in series with 9 resistor.

Step 4:

Circuit current :

Current across each resistor :

 Step 5:

Current through 6 resistor =

             = Current produced by 6 resistor due to 5 V + Current produced by 6 resistor due to 10 V

             = 0.282 + 0.440

             = 0.722