In the above right-side graph, industry's equilibrium is at e, where demand for the alligator is equal to its supply

This equilibrium point decides the price (P) that will prevail in the market and the also the equilibrium what?Quantity.

It is when supply and demand come together in a market that price and output is determined. Specifically, when a competitive market is free, price and quantity will be determined at equilibrium, which is where supply and demand are equal to each other. At this point, there is a price such that the quantity supplied and quantity demanded are equal to each other and this quantity is what will be produced and sold in the market.