Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= 6x^3-4x^2+10x-7 \\ Q(x) &= 3x^3-4x^2+8 \\ \end{aligned} $$

Step 2: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrrrr} & 6x^3 & -4x^2 & 10x & -7 \\ \color{red}{ - } & 3x^3 & -4x^2 & & 8 \\ \hline \end{array} $$

Step 3: Change ALL the signs in the second row.

$$ \begin{array}{lrrrr} & 6x^3 & -4x^2 & 10x & -7 \\ \color{red}{ - } & -3x^3 & 4x^2 & & -8 \\ \hline \end{array} $$

Step 4: Combine like terms (add each column):

$$ \begin{array}{lrrrr} & 6x^3 & -4x^2 & 10x & -7 \\ \color{red}{ - } & -3x^3 & 4x^2 & & -8 \\ \hline & 9x^3 & -8x^2 & 10x & 1 \end{array} $$

Polynomial Operations Calculator