In the last round of beta oxidation, fatty acids with odd numbers of carbons will yield acetyl-CoA and Coenzyme-A attached to a fatty acid with three carbons (propionyl-CoA)

Three enzymes are ultimately involved in activating fatty acids as fatty acyl-CoA and transferring this molecule into the inner mitochondrial matrix to be broken down via the beta-oxidation pathway. The first enzyme is acyl-CoA synthetase. This enzyme is a type of ATPase, and it uses the thermodynamically favorable dephosphorylation of ATP to drive the synthesis of fatty acyl-CoA from a fatty acid and CoASH. Fatty acids alone cannot cross mitochondrial membranes, but fatty acyl-CoA can cross the outer membrane.

Carnitine palmitoyl transferase II also synthesizes fatty acyl-CoA  but acyl-CoA synthetase is the first enzyme to do so, and its dephosphorylation of ATP is what initially activates a fatty acid.

The carnitine transport protein, known as the carnitine-acylcarnitine translocase, allows the facilitated diffusion of a fatty acid into the mitochondrial matrix. Fatty acids cannot be transported into the mitochondrial matrix alone.

Following this step, carnitine palmitoyl transferase II catalyzes the reaction that reforms fatty acyl-CoA from CoASH and the fatty acylcarnitine.

Acyl-CoA dehydrogenase converts fatty acyl-CoA to trans-Δ²-enoyl-CoA forming the high energy redox cofactor  from .

Enoyl-CoA hydratase uses hydrates the double bond between the alpha and beta carbons of trans-Δ²-enoyl-CoA by adding a hydroxyl group to the beta carbon and a hydrogen to the alpha carbon.

3-L-hydroxyacyl-CoA dehydrogenase converts 3-L-Hydroxyacyl-CoA to beta-Ketoacyl-CoA, forming the high energy redox cofactor  from . This reaction oxidizes the hydroxyl group on the beta carbon of 3-L-hydroxyacyl-CoA to a carbonyl group, and adds a hydrogen with 2 high energy electrons to .

Beta-Ketoacyl-CoA thiolase converts beta-Ketoacyl-CoA back to acetyl-CoA and a fatty acyl-CoA two carbons shorter than the original fatty acyl-CoA. The new cofactor of acyl-CoA bonds to the beta carbon of beta-Ketoacyl-CoA, and thus the beta carbon of beta-Ketoacyl-CoA becomes the new alpha carbon of the new fatty acyl-CoA. The new fatty acyl-CoA can then re-enter into beta oxidation pathway.

Of the above terms, lipase is the term specifically given to the class of enzymes that hydrolyzes fats. A ligase joins two molecules together, so it definitely could not be involved in the hydrolysis (breakdown) of fats. Proteases on the other hand are involved in protein breakdown. Kinases and phosphatases are both involved in removing and transferring phosphate groups.

Cis-enoyl-CoA isomerase has the important role of shifting a double bond in an unsaturated fatty acid to make the molecule degradable. Without this important enzyme, many unsaturated fatty acids would not be able to completely go through beta-oxidation.

Fatty acids are broken down in the mitochondria to produce acetyl-CoA. The process is called beta-oxidation. Acetyl-CoA is then used to produce energy via the citric acid cycle pathway. Fatty acids cannot cross the mitochondrial membrane directly without the use of the carnitine shuttle.The process described in the question represents the carnitine shuttle pathway, which allows activated fatty acids (fatty acids with CoA attached) to cross the mitochondrial membrane so they can be broken down by beta-oxidation. Fatty acid synthetase activates the fatty acid on the outer mitochondrial membrane by attaching a CoA group. Carnitine acyltransferase 1 exchanges the CoA with carnitine forming fatty acyl carnitine. Fatty acyl carnitine is shuttled across the membrane through the carnitine transporter. On the inner side of the membrane, carnitine acyltransferase 2 removes carnitine and forms fatty acid-CoA which can then be processed by beta-oxidation.