As some of you have pointed out, I think this scene was basically just meant to give us a bit of character development for Denise before they offed her. We were supposed to see that she's not completely helpless and that she has some kind of useful skills (aside from her medical skills of course), but the scene really just failed. He was intentionally grinding it even worse after she mentioned it, but I find the whole scenario hard to believe. It's a fair point that not all rednecks are going to automatically know how to drive a stick, but the Daryl that has been developed over the last 6 seasons does not strike me as the kind of guy who doesn't know how to drive a stick.

It's possible that it was just an old truck in bad shape, but that doesn't really make sense either. The ASZ doesn't exactly have a shortage of vehicles. Why would they choose to take out the old worn out truck with a transmission that's in such horrible shape? It makes no sense.

I think it was basically just a plot device, but it was a poor one.