Answer
$\overline{DF}=10$
Work Step by Step
$(\overline{DE})^{2}$ +$ (\overline{EF})^{2}$ = $(\overline{DF})^{2}$
$8^{2}$+$6^{2}=(\overline{DF})^{2}$
$64+36=(\overline{DF})^{2}$
$100=(\overline{DF})^{2}$
Square Root both sides
$10=\overline{DF}$