Correct option is (A) 4.5
Given that AD is angle bisector of \(\angle A\) which meets BC at D.
\(\therefore\) \(\frac{BD}{DC}=\frac{AB}{AC}\) (By internal angle bisector theorem)
\(\Rightarrow AC=AB.\frac{DC}{BD}\)
\(=6\times\frac68\) \((\because AB=6\,cm,DC=6\,cm\;\&\;BD=8\,cm)\)
\(=\frac92=4.5\,cm\)