The units you listed were actually 3 heavy support and an HQ. The zoanthropes come 1-3 in a unit, but deploy and move independently from eachother.
There's no legal way I can think of that he would be able to get 14 S10 shots from those models. As the other's have said the max is 7. The only thing that I can think of is if he was adding the extra attack from scything talons into the shooting profile, and considering the warp blast an assault X weapon instead of assault 1.
Then he would have 3 shots from each Carnifex, 4 from the tyrant and 2 from each zoanthrope = 14. If he's a new player have him read his codex more carefully, since . Pg 8 under 'Rate of Fire' and Pg 9 under 'Warp Blast'.