Flamestrike
Legend
As a DM you determine when an ability check is required and if so what the DC is.I think the argument goes that the only kinds of check that can be called for are ability checks, which can be abetted with skills. Thus the DM calls for a Constitution check (envisioning a kind of forced march swim thing going on) and allows that as the Athletics skill covers swimming, it can abet the Constitution check in this case.
I'd need to do a little more research to be 100% on this. Still, it's quite a tidy line of reasoning.
You also determine if a players skill proficiency applies to the check.
The guidance in the rules makes it pretty clear that climbing a rope (excellent handholds) generally does not require an ability check to do, as its the sort of thing that any adult human in reasonable physical condition can reliably do close to 100 percent of the time.
Doing it in a rainstorm, or with a broken collarbone, or in a hurry while under enemy fire from archers or similar circumstances might be sufficient complicating factors that might require a check.
Im not seeing the height of the climb at 6 stories being such a complicating factor because really, youre not pressed for time and can rest on the rope at will and recover your upper body strength.
The DC would be something like 0 (which is what it was in 3E) so unless were dealing with a particularly weak or frail PC, its not check worthy.