How is this possible 0 = 1

For example, let a = b
multible both sides with 'a' i.e. a^2 = ab
then subtract b^2 from both sides i.e. a^2 - b^2 = ab - b^2
then (a+b) (a-b) = b(a-b)
then remove (a-b)
it becomes (a+b) = b
now let a = 1, it become 1+1 = 1 (due to a=b in first)
so that 1 = 0 .... how does it become possible.....

Careful!

your 3rd line
a^2 - b^2 = ab -b^2 is stating 0 = 0
your 4th line
a+b*0 = b*(0) is stating 0 = 0
your 5th line
divide by (a-b) is ilegal, (a-b) = 0 and your proof fails, and 1 is not equal to zero

If you use letters in algebra, it may look logical however, in numbers anything divided by zero is infinity so it will not be possible. if you substituted the real numbers in this equation:
(a+b)(a-b)=b(a-b)
(1+1)(1-1)=1(1-1)
2(0)=1(0)
0=0 then that's the real equation

It's not
(a-b)=0 and you can't divide by 0

since a=b, a-b=0