In the Weapon X comic, Wolverine says
"I can put six shots into a quarter... an' get change for the gum-machine."
What does he mean by that? I read it here.
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I haven't read the issue in question, but the explanation seems pretty straight-forward. Shooting a hole in a quarter (that has been tossed into the air) is a common gunfighter trick in fiction; some even can shoot it more than once. Many famous marksmen have claimed to do it; Annie Oakley being one of the better known ones. Claiming to be able to do so (or some fancier version, as Wolvie does) is a common gunfighter's boast.
Six is a bit excessive, but from the same Marvel Wiki article on him that you cite:
Expert Marksman: He is an expert marksman skilled in throwing weapons and firearms, but operates more efficiently without them.
The comment about change for the gumball machine is a common piece of bravado added to such claims; it takes many forms. He's talking about 'breaking' the quarter the same way you 'break' a dollar into change; he's just saying it to be silly/dramatic.
Oh, you kids today! It's a meme, basically the same as X all the Things! but older.
I would say that the "original" is, "Stop on a dime and give you change." but I can't find any cites for that. There are many variations, just as there are with modern memes.
Saying that - for example - a car can "stop on a dime" is a boast about how good the car is. A dime is about a centimeter in diameter (it's the smallest size of any US coin), so claiming that your car can stop in that short a distance is already a boast. Adding the "give change" makes the boast stronger, by claiming that the car can stop in an even shorter distance.
TL;DR: Logan is boasting of his accuracy with a pistol, of being able to place six shots in a diameter smaller than a US quarter-dollar coin.
In marksmanship, the term "spread" refers to the distance between each bullet impact. Ideally, you want the smallest spread possible for the greatest precision & accuracy:
What Logan means when he says "I can put six shots into a quarter... an' get change for the gum-machine." is that he can shoot the quarter six times without nicking the edge - possibly even in the same place. Most gumball machines of the era measured the diameter & edge of a coin to determine if it was a quarter or not. Therefore, a quarter full of holes would still work in the machine. Gumballs of the time were commonly only a nickel, so he would get his gumball plus two dimes back as change. The weight of the coin could be a factor too (depending on the machine), so this could also indicate placing bullets in almost exactly the same spot all six times (leaving only one hole in the coin).
Note: Coins have long been used to show off precision with a firearm. The American sharpshooter Annie Oakley was famous for her trick of flipping a dime into the air and shooting it with her pistol. Despite the similarity, however, that was a trick meant to show her accuracy with a moving target. Logan is instead boasting of his small target spread.