Dr Peterson showed you his way and it was excellent.
Here is my way. Instead of writing x as x, I write x as ( ). That is, wherever I see x, I write ( ). OK
We have f(x) = 4x2 + 4x - 3. So what I write is f( ) = 4( )2 + 4( ) - 3.
Now if they want me to find f(a), I go back to my last line and place a in all the parenthesis.
We have f( ) = 4( )2 + 4( ) -3 and it becomes f(a) = 4(a)2 + 4(a) -3.
Note that I did NO mathematics at all. I like to call it art work. All I did was replace all x's with ( )'s and then I put in between all the ( ) exactly what the problem had between the ( ), namely a.
Now the math starts. You need to simplify 4(a)2 + 4(a) -3 and multiply this result by 2.
In my opinion, what students find the hardest, finding f(something), is the easiest part if you do it in a way that you understand.
In this thread you have been giving two ways to do the start of problems like this. Either do it one of these two ways or figure out your own technique. If you do not understand how your teacher does it, that is fine. However that does not mean that you can't go ahead and figure out your own method/style.
Post back with your work.