Ana Maria needs to convert this scale drawing from a scale of 1 box = 4 inches to a scale of 1 box = 2 inches. The width in the scale drawing shown is 3 boxes.  What will be the width in boxes of the new drawing?

If 1 box represents 4 inches, and the width is 3 boxes, then the width is 3 * 4 = <<3*4=12>>12 inches.

If the new scale is 1 box = 2 inches, then the width in boxes will be 12 / 2 = <<12/2=6>>6 boxes. Answer: \boxed{6}.