He made an error in step 1. Specifically, he distributed incorrectly.
The 3(x+2) portion is not the same as 3x+2. We need to multiply that '3' by the 2 as well to get 3*2 = 6
In other words, 3(x+2) should turn into 3x+6
If you wanted, you can think of 3(x+2) as three copies of (x+2) added together like this: (x+2)+(x+2)+(x+2) = (x+x+x)+(2+2+2) = 3x+6
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Check out the diagram below to see how his steps should look like. I basically started with what your teacher gave you, but changed a few things as shown in red.
