Given that,

$(8x+4)$, $(6x–2)$ and $(2x+7)$ are in A.P.

Therefore , the common difference between the consecutive terms is same.

$(6x–2)$ $–$ $(8x+4)$ $=$ $(2x+7)$ $–$ $(6x–2)$

⇒ $6x–2–8x–4=2x+7–6x+2$

⇒ $-2x–6=-4x+9$

⇒ $-2x+4x=9+6$

⇒ $2x=15$

Therefore,

$x=15/2$