Answer
$(t-4)(t-6)$
Work Step by Step
$-10$ is negative, so we list negative factors of $24$.
$\left[\begin{array}{llll}
\text{ Factors of 24 } & \text{Sum of factors}-1 \text{ and }-24 & -25 & \\
-2\text{ and }-12 & -14 & \\
-3\text{ and }-8 & -11 & \\
-4\text{ and }-6 & -10 & \text{...is what we need}
\end{array}\right]$
$t^{2}-10t+24=(t-4)(t-6)$
