In the 5e PHB, the Variant: Skills with Different Abilities topic confuses the hell out of me.
Your DM might call for a Constitution Check… Your DM might allow you to apply your proficiency in Atheletic and ask for a Constitution (Athletics) check… so you apply your proficiency bonus to the Constitution check just as you would normally do for a Strength (Athletics) check.
So does that mean that if I had +4 in Stength, +1 in Constitution and +2 proficiency bonus, then my Atheltics would be +6 with proficiency. If I made a Constituion (Athletics) check, would it be a 1d20 +1(Constituion) +2(Proficiency bonus)?
If so, if I had a +4 Strength, + 1 Charisma and +2 proficiency bonus, then my Intimidation would be +3 with proficency. Does that mean If I made a Strength (Intimidation) check, I would roll 1d20 +4(Strength) +2(Proficency bonus)?
This variant rule confuses me. I know I don't need to use it but I want to understand it in case I do want use it in the future.
If I made a Strength (Intimidation) check, I would roll 1d20 +4(Strength) +2(Proficency bonus)?
This is correct.
The skill and attribute combinations printed on the character sheet are the most common applications of skills that turn up in the game. 99% of the checks you make will use those combinations. But the rules are the same for different combinations.
Here are the two relevant rules:
The formula is always the same. When you are proficient in the skill the DM calls for, the formula is:
In this question about hiding a body, I suggest a few alternative skill checks. Maybe seeing other examples can clear things up: What are the mechanics for hiding something that is not yourself?: