i know that i didn't use the superposition theorem properly. It's my own method to analyze very simple circuits by inspection.He's describing the concept of superposition, but not doing so correctly or validly. You don't "neglect" the sources, you turn them off (i.e., set them to zero output). For a current source, this means effectively removing it from the circuit. But for a voltage source it means shorting it so that it have 0V across it but no restriction on the current rhrough it.
That his method is invalid is evidenced by the fact that it produces the wrong answer for this problem. He gets 1A flowing downward in the 1R resistor when neglecting the current source and 8A flowing downward in it when neglecting the voltage source for a total of 9V. But, used properly, superposition gives 1A flowing downward with the current source turned off and 6A flowing downward when the voltage source is turned off.
the current from current source (only) will divide into four parts i.e 2+2+2+2. The first three part will flow from 1 ohm resistor while one part will flow from 3 ohm resistor. and we also know that the current due to voltage source alone is -1 A in the direction of I4. when i can clearly see the current then there is no need to include that 3 ohm resistor in the solution. so i removed it along with voltage source.