Yo can prove that this set of equations is equivalent by applying some math operations on one of the equation and making it look like the other one.
In this case, we could transform the second equation x+3=2 into the first one (3x+9)=6 by multiplying both sides of this equation by 3, like this:
x+3=2
3*(x+3)=3*2
3x+3*3=3*2
3x+9=6
As you can see, now the second equation look exactly the same as the first one, then we can say that this pair of equations is equivalent