An Even-Even graceful labeling involves assigning even labels to both vertices and edges in a graph. The goal is to create a labeling where vertex and edge labels are even integers, and the differences between vertex and edge labels form a set of consecutive positive even integers. This concept explores the relationship between numbers and graph structures and has potential applications in computer science, optimization, and network analysis. This paper demonstrates some new results on Even-Even graceful labeling of m star graphs for m = 4, 5, 6. Additionally, it is shown that double, triple, and quadruple extended star graphs are Even-Even graceful under certain conditions, as discussed in this paper.