This is quite a difficult question to answer because it really depends on the individual. It is possible but you won't be able to build large muscles if you are starving yourself of carbs in the hope of burning fat at the same time. On the flip side, if you eat quite a high carb diet, then your body will have plenty of fuel to store as fat, unless you are doing a lot of exercising to burn it off. So it's quite a difficult question to give a definitive answer to.

Lets look at each side of the argument and then try to determine the best route to take.

Building Muscle

The principal is simple, you create a calorie surplus, which means you have more calories that can be used to build up your muscles. If you don't workout often enough, the surplus calories will be stored as fat . So you will almost certainly gain weight but not all of it will be muscle.

Burning Fat

Again, a simple concept. This time you create a calorie deficit, which means you don't give your body enough fuel that it needs. This forces it to use fuel that is already stored in the form of fat. If you do aerobic exercise, then you will burn quite a lot more calories than you consume and should lose weight quite quickly.

So How Do You Combine The Two?

The only way this can be done is all in the diet. You need to keep up a mid-high level of carbs to increase your muscles but not too many that cause your body to store them. So you should only eat foods that can be quickly digested by the body and that are also used for muscle growth. By having a good balance of bodybuilding, to build the muscles and aerobic training to burn off the excess calories that aren't used, is the only way you can burn fat & gain muscle at the same time.

It is possible but will take some careful planning and monitoring.