A perfect star packing in a fullerene graph is a spanning subgraph whose every component is isomorphic to the star graph \( K_{{1,3}} \). A perfect star packing in a \( {(3,6)} \)-fullerene graph is called a perfect star packing of type \( T0 \) if no center of a star is on a triangle of \( G \). A \( \mu \)-way \( G \)-trade consists of \( \mu \) disjoint decomposition of graph \( H \) into copies of graph \( G \). In this paper, we use the concept of packing and specify values of the number of copies of \( G{=}S(K_{{1,3}}) \) for which there exists a \( \mu \)-way \( S(K_{{1,3}}) \)-trade when the underlying graph is a non-trivial \( {(3,6)} \)-fullerene graph.