CAN I LOSE WEIGHT WITH WEIGHT TRAINING AND CARDIO?

I have a friend who is between the age 45-50. She told me that she had been doing weight training & cardio ( but never changed her diet ) and never lost any weight or inches with that program. She complained to her son about it and he told her that the fact that she was working on the weight machines was her problem and that if she did strictly cardio, then she'd lose weight. She took his advice and said the pounds melted off. She lost about 32 pounds in a 12-month period, but again never changed her diet.

I have a hard time believing that if you do light weight training along with cardio that you won't lose weight because the more muscle you build, the more fat you burn. I'm telling this story because I am also in that age group and am working on the weight machines. I joined a new gym a month ago and was told by their staff that I should lift weights for upper body one day, lower body & abs the next and alternate, which I already knew and that I should do that first, then do my cardio. They also said that I should have just one day of cardio w/o weights.

So, if I continue that workout program AND cut out fat, sugar & carbs and stick to fresh veggies and some fruit & lean meat, shouldn't I be able to lose weight and quicker than 32 pounds in a year? Thanks for your help - and if you have more suggestions give them to me. I'm actually looking to lose at least 15-20 pounds in a 6-week period, or at least lose 2 dress sizes.