The property of some metabolic pathways that enables them to serve multiple functions in the breakdown, synthesis, and conversion of metabolites is known as .

The property of some metabolic pathways that enables them to serve multiple functions in the breakdown, synthesis, and conversion of metabolites is known as amphibolism.

Explanation:

Amphibolic pathways are the biochemical pathways which have both catabolic (breakdown ,conversion to metabolites)  and anabolic functions (synthesis)

For example:  

The property of some metabolic pathways that enables them to serve multiple functions in the breakdown, synthesis, and conversion of metabolites is known as amphibolism.

Explanation:

Amphibolism are all intermediate reactions, where catabolism meets anabolism. Catabolism are the "degradation" reactions, that is, starting from large complex molecules (carbohydrates, lipids, proteins) from food or from reservoirs, simple molecules are produced (lactic acid, CO2, NH3...) intermediates of numerous metabolic reactions (metabolites). These reactions yield energy in the form of ATP. On the other hand, anabolism is the set of metabolic reactions in which more complex molecules are synthesized from simple compounds. These reactions consume the energy contributed by the ATP generated in catabolism. Amphibolism or intermediate metabolism, is the set of reactions in which the hydrolysis products of catabolism and some nutrients are transformed into organic acids, phosphoric esters and other compounds as amino acids, that is, both processes of degradation (breakdown) and synthesis of molecules are presented, there is a mutual regulation.

try using substitution:

x + y - 6 = x - y. (i'm not giving you the exact answer). since 0 = x - y, then sub 0 in the equation with x - y. combine your like terms, and then use inverse operations, and you'll have your answer.

: -)