Based on reading some of the websites it seems that their hypothesis is that because ALC is involved in the Krebs cycle in the mitochondria, which gets energy from fatty acids, that means ALC helps burn fat. There is not much in the scientific literature on this topic, but I did come across an article that found no difference in metabolic parameters in study participants taking L-carnitine versus controls (not exactly the same things as acetyl-L-carnitine, but they are used somewhat similarly in the body, there just isnt the extra acetyl group in the L-carnitine)
Die Carnitin 1000 Trinkampulle enthlt 1000 mg reines L-Carnitin und ist B-Vitaminen sowie Zink und Magnesium angereichert, um den Energiestoffwechsel weiter zu untersttzen
The organosulfur compounds present in the aqueous and alcoholic extract of garlic include S -allyl cysteine (SAC), S -allylmercapto-L-cysteine (SAMC), and S -methyl cysteine (Figure 1C)
In: FASEB journal: official publication of the Federation of American Societies for Experimental Biology
In: Stipanuk MH, ed
(Rome, Italy), the pioneer in L-Carnitine science