Wolfgang wants to enlarge a picture he developed. which factor listed below would scale up (enlarge) his picture the most if he used it to multiply its current dimensions? 7/8 14/14 1 4/9 3/2

You want the largest number here. Both 14/9 and 3/2 are greater than one, so the other options can be eliminated. You can either convert to decimals, or put them over a common denominator.
For decimals, divide 14 by 9 to get 1.556. Then divide 3 by 2 to get 1.5.
If you want to stay in fractions, put them over a common denominator (18 in this case). 14*2->28/18. 3*9->27/18. In both cases, 14/9 is greater so you know your math is correct. 14/9 is the answer.