in this sum the option b in that in left side it was multiplied by 2 but in the right only to one of the x-2 and not x+2 is that okay i thought the operations are supposed to be performed at all
Yes, multiplication is being applied to both sides.
If we multiply the left hand side by 2, we get 2(10y^2) = 20y^2.
If we multiply the right hand side by 2, we get 2(x+2)(x-2) = (2x-4)(x+2). The 2 does not get distributed to both (x+2) and (x-2) but rather is distributed to only one of them. If it were distributed to both, then the equation would not hold true:
2(x+2)(x-2) does not equal (2*(x+2))(2*(x-2)) because factoring out both 2’s, we would get 4(x+2)(x-2).
Try plugging in numbers to see that those quantities are different. I hope that helps!