Sugar Twin and other artificial sweeteners are low or no- carb, but the 4 slice of bread contain a total of 60 to 100 grams of carbs and 240 - 400 calories. For people who are very carb sensitve, it can be very difficult to lose weight without keeping carbs pretty low.
For myself, if I eat much more than 100g of carbs, I find my weight loss is unreliable and not always consistent with my calorie level (I think how on earth could I possibly not be losing on so few calories). I can lose weight on low-calorie high carb diets, but I'm hungry all the time and the weight loss isn't steady or consistent - there's a lot more ups and downs on the scale from water retention. With low-carb (for me under 100g) my weight loss is more consistent despite being able to eat more calories, and my hunger is more manageable.
Reducing carbs to super low levels (less than 20g) gets rid of hunger, I lose much more consistently, but at the expense of side effects I don't want to deal with, so I stick with moderate low-carb from 80-100g (some people say they have difficulty losing on even this many carbs).
Also, calories still matter (whether you end up having to count them or not). Even on Atkins induction level carbs (fewer than 20g total), my weight loss will stall if I don't have a portion-control plan (in my case an exchange plan that contains no more than 1500 - 2000 calories).
My plan allows 3-4 fruit and 2-3 starch exchanges for the day (a large apple counts as 2 fruit, and one ounce of bread, half an ounce of cereal, or 1/2 of a potato counts as 1 starch exchanges).
I don't know if you're eating potatoes, rice, pasta, corn, carrots, beets, peas, parsnips, squash or fruit but those all contain carbohydrates as well, which you may have to watch if you're carb-sensitive.
Most non-starchy veggies have minimal carbs because most of the carbs are fiber, which humans can't digest, but you've got to know which ones are higher carb, if you want to control carbs, and some people argue that you still have to watch net carbs (I've never had to count non-starchy veggies).