Let's take the easier equation y=3x+2 and see what happens. This is a line with slope 3 and y-intercept 2.
You said stretch by 1/3 parallel to x-axis (so x'=3x and y'=y). The y-intercept will not change, but the slope changes from 3 to 1, and the equation is y=x+2. (I'm being sloppy and dropping the primes as I go.) Now you translate 2 units to the left (so x'=x+2 and y'=y), and the equation is now y=x.
If you had translated by 2 units first, you would have y=3x+2 going to y=3(x-2)+2=3x-4, and then the stretch would give y=x-4, which is not what you want. However, if you recognize y=3x+2=3(x+(2/3)), and you translate by 2/3, then stretch, you'll get the right answer.
I hope this clarifies the order of stretching and translating. Post again if you are still having trouble.