| Bob Hope |
So if we imagine before resistances, you have 6 slashing and 5 bludgeoning damage. Those are combined into a single instance of damage, but each type will have the highest resistance applied. So in this case, the slashing is reduced by 5 (leaving 1) and the bludgeoning is reduced by 2 (leaving 3) and the creature takes 4 damage.
If that creature casts Mountain Resilience, they'll have 5 resistance to bludgeoning, piercing, and slashing. For the bludgeoning resistance, we'll use this higher value instead of the 2. That means the same attack that did 6 slashing and 5 bludgeoning will only end up doing 1 point of damage.
This is a little strange, because it makes the warhammer a much better option when overcoming resistances (or a piercing weapon with a piercing shield boss). Doing 6+5 bludgeoning would mean only the 2 bludgeoning resistance is applied, and the creature would take 9 damage (or 6 damage if they had the Mountain Resilience).
There was a sample play session with some of the designers, and this is how they dealt with resistances to multiple damage types. It's also covered in the Resistance rule section where they talk about resistance to all damage.
The way I think about this mechanic is that your damage is put in different bins based on damage type, and each bin is drained according to the resistance. Then the bins are combined and applied.
Edit: Here's a better source.