There were four at the actual battle of Midway, the 4 that that USA killed.
So it is correct to say there were 4 Japanese carriers in the active battle zone
Zuiho — and the main invasion force — never got close enough to the actual kill zone where the combat took place
the US admirals withdrew back towards Pearl Harbor to avoid a night engagement on June 4th
The Japanese advanced with the main fleet briefly during the night — hoping to lure the US carriers —
but IJN realized their battleships and any carrier with the main invasion fleet would be vulnerable to both the US carriers as well as the attack aircraft on the atoll — so they slunk back to Japan at daylight on June 5
My goal was to sink the main four and then go for the ultimate goal of sinking the Zuiho with either US task force. I only got her once.