If a spell or ability damages multiple things, divide up the damage before applying this effect. This means you can't normally end up with an odd amount of damage on something.

The trample rules cause damage to be divided before it is doubled.

If you have two of these on the battlefield, the damage is multiplied by 4.

The multiplied damage counts in all ways as if it came from the original source. Furnace of Rath is not the source.

If multiple effects modify how damage will be dealt, the player who would be dealt damage or the controller of the creature that would be dealt damage chooses the order to apply the effects. For example, Mending Hands says, "Prevent the next 4 damage that would be dealt to target creature or player this turn." Suppose a spell would deal 5 damage to a player who has cast Mending Hands targeting himself or herself. That player can either (a) prevent 4 damage first and then let Furnace of Rath double the remaining 1 damage, taking 2 damage, or (b) double the damage to 10 and then prevent 4 damage, taking 6 damage.