More exercise, less calories, smaller portions. Do any of these, preferably a combination of 1 or more,and you will lose weight, anyone will.
Bananas - no question, good for you.
Vinegar - no evidence that it can "burn fat" or aid in burning carbohydrates. Fat is not stored in blood cells.
There are some hypothetical mechanisms by which acetic acid may interact with process of burning calories, but thats all they are. There are some animal studies in mice that are suggestive that maybe acetic acid plays a part in the fat metabolism, but those studies are few and far between, small in scale, and have little relevance just now to human metabolism.
If you want to drink vinegar, go ahead - but it is unlikely to do anything significant :)
Stick to cutting out unneccesary carbs and fats, smaller portions, more exercise and you will lose weight.