Carnitine facilitates the transport of fatty acids into the mitochondria to be used in fatty acid metabolism. It does so by accepting acyl groups from fatty acids complexed with coenzyme A, which yields esterified carnitine or acylcarnitines that enable the transport of fatty acyl groups into the inner mitochondrial matrix. β-Oxidation of fatty acids in mitochondria is inhibited by uncoupling conditions, thus changes in circulating levels of various acylcarnitines have been used to identify alterations in metabolic state.[1] [2] Arachidonoyl-L-carnitine formed from carnitine conjugated to arachidonic acid .

Reference:
[1]. Osmundsen, H., Cervenka, J., and Bremer, J. A role for 2,4-enoyl-CoA reductase in mitochondrial β-oxidation of polyunsaturated fatty acids. Effects of treatment with clofibrate on oxidation of polyunsaturated acylcarnitines by isolated rat liver mitochondria. Biochemistry Journal 208(3), 749-757 (1982).
[2]. Sampey, B.P., Freemerman, A.J., Zhang, J., et al. Metabolomic profiling reveals mitochondrial-derived lipid biomarkers that drive obesity-associated inflammation. PLoS One 7(6), e38812 (2012).