The first two hints can be expressed as the following system of equations:
$$\begin{cases} (1) & a + b = 6 \\ (2) & a - b = 8 \end{cases}$$
From this, we can clearly see that $a = 7$, and that $b = -1$.
Since quadratic equations can generally be expressed in the form of $(x - a)(x - b) = 0$, where a and b are roots, the correct quadratic, once factored, would look like $(x - 7)(x + 1) = 0$
Expanding the above equation gets us $\textbf{(B)} x^2 - 6x - 7 = 0$