A global forcing set in a simple connected graph with a perfect matching is any subset of such that the restriction of the characteristic function of perfect matchings of on is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number of . In this paper we prove that for a parallelogram polyhex with rows and columns of hexagons () the global forcing number equals if is even, and if is odd. Also, we provide an example of a minimum global forcing set.