Each instance of the ability would go on the stack one at a time.

So the first 8/8 hydra attacks and puts his ability on the stack,

The second hydra's ability goes on the stack,

The Doubling season's replacement effect modifies them each time the hydra's ability triggers.

Since you are the active player and they both trigger at once, then you get to decide what order they go onto the stack, even though in this case it does not much matter because they both do the same thing.

The first hydra doubles the counters, since it is going to put counters on something and the Doubling season says to put twice that many on, they end up with 8 + 16 =24 counters instead.

The second hydra doubles the counters, since it is going to put counters on something and the Doubling season says to put twice that many on, they end up with 24 + 48 = 72 counters instead.

so they are 8 +16 = 24 then they are 24 + 48 = 72.

614.1a Effects that use the word "instead" are replacement effects. Most replacement effects use the word "instead" to indicate what events will be replaced with other events.

Each instance of the ability would go on the stack one at a time.

So the first 8/8 hydra attacks and puts his ability on the stack,

The second hydra's ability goes on the stack,

The Doubling season's replacement effect modifies them each time the hydra's ability triggers.

Since you are the active player and they both trigger at once, then you get to decide what order they go onto the stack, even though in this case it does not much matter because they both do the same thing.

The first hydra doubles the counters, since it is going to put counters on something and the Doubling season says to put twice that many on, they end up with 8 + 16 =24 counters instead.

The second hydra doubles the counters, since it is going to put counters on something and the Doubling season says to put twice that many on, they end up with 24 + 48 = 72 counters instead.

so they are 8 +16 = 24 then they are 24 + 48 = 72.

614.1a Effects that use the word "instead" are replacement effects. Most replacement effects use the word "instead" to indicate what events will be replaced with other events.

The comprehensive rules show that each ability would count the number of counters at the time it resolves, not when it is put on the stack. (Emphasis mine)

608.2g If an effect requires information from the game (such as the number of creatures on the battlefield), the answer is determined only once, when the effect is applied. If the effect requires information from a specific object, including the source of the ability itself or a target that's become illegal, the effect uses the current information of that object if it's in the public zone it was expected to be in; if it's no longer in that zone, or if the effect has moved it from a public zone to a hidden zone, the effect uses the object's last known information. See rule 112.7a. If an ability states that an object does something, it's the object as it exists -- or as it most recently existed -- that does it, not the ability.

In this case the information from the game the Hydra's ability needs, is the number of counters on each creature who's counters are being doubled.