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I am 24 years old and have a 5 month old daughter and a 2 year old son with special needs. I have struggled with weight my entire life and I am now determined to lose 45 lbs. I have lost all of the pregnancy weight that I gained and a couple of extra pounds. I do not have time to actually go to a gym due to my son's care but I just received P90X and Zumba fitness in the mail. Any advice and tips is greatly appreaciated and very much needed.

Welcome to the forum! It sounds like you have your hands full and it is great that you got some dvd's to help you get some exercise in.
My advice would be to find a food plan that fits in your lifestyle and that you can stick to long term. There is a ton of information on this site which can help you make a decision. I choose calorie counting, it is free and there are a ton of free apps to help you track your calorie intake.
Make small changes first. Like drinking more water, exercising a couple times a week, eat more fruit and veggies, all small changes add up.
Most of all, if you fall off plan, do not give up. We are not perfect and will make mistakes.
Best of luck to you.