You can put this solution on YOUR website!
Figure A: 4 + x = 4 + 1x.
That's so true. I guess your teacher is trying to point out that when you write a variable by itself, there really is a 1 being multiplied to it, but you don't really write it. The mere presence of a single variable automatically means that there's one of it. If anything else, you would have to say 2x if there were really 2 x's.
Figure B: 4 + x = 4x <----- INCORRECT
Four plus some number does not mean to multiply 4 to whatever that number is. That's like saying 5 + 6 = 5*6, which is obviously wrong.
I'm not sure what you mean by "do it as in figure B".