Finding the greatest common divisor of two polynomials in a ring

Question

I am trying to find the greatest common divisor of two polynomials in $\mathbb Z_7$. I have attached the beginning steps as given by my professor. I have done several examples of the same type and I know what I am doing, but for some reason I always run into the same problem in the first step. When multiplying $g(x)$ by $4x^2$, I get $24x^6+4x^5+8x^3+14$ and then I convert to $\bmod7$. So $24=3\mod7$, $8=1\mod7$ and $16=2\mod7$. This gives $3x^6+4x^5+x^3+2x^2$. However for some reason in every answer others give me, $8x^3$ becomes $4x^3$ and nobody can explain to me why that is so. The rest of the problem works fine if I carry on this way. I am confused with what simple mistake I must be repeating. Nobody has been able to give me a solid answer yet. https://i.stack.imgur.com/z7Mzw.png