A fullerene is a polyhedral molecule made entirely of carbon atoms other than graphite and diamond. Mathematical chemistry or Chemical graph theory as a combination of chemistry and graph theory studies the physical properties of mathematically modeled chemical compounds. Graph labeling is a vital area of graph theory that has applications in both physical and social sciences. For example, in chemistry vertex labeling is used in the constitution of valence isomers and transition labeling to study chemical reaction networks. A (4,6)-fullerene graph is a mathematical model of a (4,6)-fullerene molecule. It is a cubic-regular planar graph whose faces are squares and hexagons. In this article, we study the total vertex irregularity strength and the total edge irregularity strength of a disjoint union of (4,6)-fullerene graphs and provide their exact values.