The new string only goes through the tuning peg one time. One way that may help when tightening the string is to, after putting the string through the hole, use your left hand to hold down the string at the nut of the guitar (around the 1st fret) and push down on the string in between the nut and the tuning peg. This way you'll force the string to go as low as possible onto the tuning peg. I'll try to create a video lesson on this for you that may help.