Take your squad to the designated marker to start this mission which, and let's be honest with each other here, doesn't make a lick of sense.
Mixer calls asking you to boost a sweet ride for him. Disregarding that there's nothing on the street sweeter than your AI wheels, and he surely makes enough to at least rent something nice, and stealing is wrong, etc. Follow your marker to a car with a purple driver's wheel icon above it. Note that this can be any type of car (it changes each time you play the mission), and it may not actually be at the objective point. Disregard also that your objective sez to steal a car for Quartermile, when it's clearly Mixer who you're felonizing for.
When you get in, LEGION soldiers will appear. Ignore them- they spawn endlessly. Just drive for the checkpoint, doing your best to avoid enemy attacks, both ballistic and vehicular. This is easier for some cars than other, but not to worry- if the car blows up, you just start the mission over. When you reach the checkpoint, do not just park under the green indicator arrow. Drive those extra few feet to park atop the AoM logo.
Only it doesn't matter anyway, because your next objective is to pick Pat up yourself. Swell. Kill the LEGION goons at the dropoff point here, then drive over (with your real car) and kill the goons waiting at the pickup. There aren't many, and the floating objective marker will track them if they flee.
Now you need to rescue Pat, because LEGION has kidnapped her, apparently with the sole aim of annoying you. Well, mission accomplished.
Take to the rooftops to gun down some minimal resistance, and get eyes on Pat, who's tied to a bomb.
Get close enough to use the interact key to save her. She'll glow purple, but still be attached to the bomb, which makes it seem strange that your next objective is to destroy the bomb.
Still, destroy it you must. Once that's done, Pat bounces free and a bit of dialogue will play, completing this mission, and unlocking Kingpin's first outing.