Notice how
2x-5 = 2x - 2*2.5 = 2(x-2.5)
This means we can replace x with x-2.5 in the second step, in the "wrong way" column.
So,
y = ln(2x)
y = ln( 2(x-2.5) )
y = ln( 2x - 2*2.5 )
y = ln( 2x - 5 )
In the second step, the x-2.5 tells the reader to shift the curve 2.5 units to the right. Therefore, the 1/2 = 0.5 would shift to 0.5+2.5 = 3 as indicated by the correct graph.
