On page 67 of New Moon, this is what we are told about Edward's car:

"He was parked in Charlie's spot when I pulled up in front of the house."

Then, Edward and Bella go into the forest and he says goodbye. There is no mention of his car and no possibility that Edward moves it in between Bella seeing it parked in front of her house and Edward leaving on page 73. The line on page 73, from just after Edward has left is as follows:

"I followed him into the forest." (Bella narrative)

Into the forest would have taken Edward in the opposite direction to his car. When Bella returns to her house, much later that night, Edward's car is not there. (We are not actually told that his car has gone but Bella would definitely have noticed it if it was still there). Edward would not have risked going back to the house to retrieve his car after leaving in case he ran into Bella again. Bella however, never sees Edward's car after their parting so where did it go? How did Edward's car get away from Bella's house?