Every head of the Hydra breathes once, for 15d6 damage each. However, you should probably run this as if
The Hydra breaths once, for 15d6 damage
These reddish hydras can breathe jets of fire 10 feet high, 10 feet wide, and 20 feet long. All heads breathe once every 1d4 rounds. Each jet deals 3d6 points of fire damage per head.
The first sentence just tells us the dimensions of each jet, which are similar to but distinct from a "line".
The second sentence tells us that all of the heads breathe once every 1d4 rounds. A strict reading thus requires all of the heads to breathe simultaneously, as a round-triggered event.
The third sentence tells us that every jet the hydra produces deals 3d6 points of damage per head the hydra possesses. It does not indicate that any heads but the one producing the jet are used in the production of the jet, just that the damage scales with the number of heads.
This is a lot of damage for many-headed hydras. A twelve headed cryohydra, for example, focusing all of its wrath on a single adventuring party of targets fitting in a 10X10X20 foot line would deal 432d6 cold damage to each of them. This is enough to guarantee a one-shot kill on an equivalently sized pyrohydra. It is also the largest source of cold damage available in the rules, without epic spells (and it's better than most of those, too). Given that this creature is supposed to be CR 13, this is probably not how the hydra is supposed to work.
When I play in or GM high-op games, this high damage output tends to be used, and pyro/cryo hydras are combat monsters of the highest caliber (indeed, half-black dragon half-white dragon 12-headed pyrohydras and their icy half-red dragon half-green dragon counterparts show up much more often than one would expect, given their odd genealogies).
When I GM mid-to-low-op games I explain to my players that the 'per head' phrase at the end of the sentence is a typo resulting from redundancy, and that actually each jet just does 3d6 damage, with all of the heads breathing once every 1d4 rounds. This results in the 15d6 damage total I suggest you use. Remember not to forget the multiple saves, which mitigate the damage output into roughly the expected range for the hydra's CR (it's still above average power at nearly every level!).