Sentence with multiple 'and's: should I use an Oxford comma, and if so, where? [closed]
Solution 1:
The serial comma only comes into play if you have an actual list, i.e. three or more items. You only have two:
excellent problem solving ability
and
outstanding coordination and communications skills
To see this, look at the nouns, not the phrases describing them: ability and skills are two things.
Within the phrase "outstanding coordination and communications skills", it is absolutely wrong to insert a comma before the "and". For the sentence as a whole, though, the issue isn't quite so clear-cut: it's not really a list, so adding a comma is unnecessary, but on the other hand, it can aid comprehension to group the adjectival phrases — basically, to make it clear that excellent problem solving goes with ability, while outstanding coordination and communications all go with skills.