The cleanse puts a lot of burden on our systems, if your daughter is wanting this for weight loss I would say that this is not motive enough to put her body through this. At 14, young adolescents do not have the frontal cortex matured enough to think through the total ramifications and or reasoning to undertake a very strict regimen such as the MC. My sense is that she might want to try this extreme method for instant weight loss. The problem with this is multi layered: first if she does undertake this her metabolism will slow to a snailís pace and will make losing weight in the future more difficult. She will have to exercise very hard to reset her metabolism and it will not necessarily be the same and can get more sluggish than pre-cleansing. Second this is a red flag alert for me to wonder if she is pre-disposed or already setting herself up for an eating disorder. Third does she have a plan that she can stick with afterward? If she feels the need to cleanse, what changes will she make after so that she does not get so toxic? I have two teens 16 and 19, my 19 year did this when she was 16 but she made a very conscious choice with all of these factors considered. She only lasted 4 days because it caused so much stress on her system. She did decide in the end to become a vegan, she was already a vegetarian and found that the vegan life style was a better fit for her and a way to boost her energy, metal stamina and overall sense of well being.
I hope this helps some to help guide your teen to making good choices for herself in the future.