Don't eat like that if you can't exercise. If you want to see your abs without exercise, fats, carbs and protien will serve less of a purpose. The abs diet is specifically intended to accompany and compliment a good exercise program. If you can't exercise, don't do an exercise based diet program.
Eat an apple (/pear/orange/grapefruit/etc.) and one cup (an actual cup, not whatever amount of milk fills your particular container) of nonfat vitamin enriched milk. Drink plenty of water bewteen breakfast and lunch. For lunch have a small sandwich with nonfat meat and notfat cheese, with some fresh veggies like lettuce, spinach, tomato, and such. With that have some water. Drink plenty of water between lunch and dinner, but don't snack. If you absolutely HAVE to snack, take some walnuts and raisens. I know it sounds gross, but after maybe a day they'll be delicious. For dinner make a salad with no dressing (do not use low carb/low fat dressing, as it is more unhealthy than regular dressing) and if you want, add some chicken or fish. No crutons. Try to get as much variation in the veggies of the salad as possible. Don't starve yourself, but eat until your full and stop until your next meal. Do not splurge.
The abs diet is intended for someone who has a good solid exercise program to burn off all the fats and carbs you take in. Without the exercise, that potential energy becomes fat to be stored for later use. That's why you are gaining fat. Have you ever looked at the nutrition facts on the peanutbutter container? Mine has 17g of fat per serving (1 serving = 32 grams) and 3.5g SATURATED fat. That means more than half of the peanut butter you are eating is fat, and more than 1/10 is saturated. That is ETREMLY unhealthy. The only reason you see diets contain peanutbutter is because you'll be burning iot off with strenuous exercise later, so you don't have to worry as much about it becoming fat.
If you have back problems, you might consider a sitting treadmill. You always must exercise. The only excuse for not exercising is amputation or parilization.
I hope I was helpful, and best luck on the diet