We will use the principle of the similar triangles.
Triangle ABC was dilated and rotated to form triangle DEC
So, the triangle ABC is similar to triangle DEC
∴ [tex]\frac{AB}{DE}= \frac{BC}{EC} = \frac{AC}{DC} = constant = m[/tex]
BC = 8 and EC = 5 ⇒⇒⇒ So, [tex]m=\frac{8}{5}[/tex]
∴ [tex]AC = m * DC = \frac{8}{5}*6 = \framebox{9.6}[/tex]
