I have 11k fighters in APC for the battle. But the battle report show only 4k plus are fighting?

Not sure how you see in the battle report the number of troops taking part. You can see the number wounded etc.

Possibly if it was an easy win then not all troops were needed. Alternatively if it was a defeat then the game does have a mechanic that causes the morale of the formation to fall when being beaten and the remaining troops will abandon the fight and retreat (you lose the fight) if the losses are too heavy. This stops you losing too many troops in one battle. I don't know if these explain it or if there was an issue.

Only 40% of troops fight in battle, my guess is so you don't lose all your troops in 1 fight. If all troop were to fight your hospital would fill up pretty quickly.