A compact hyperbolic surface of genus g is said to be extremal if it admits an extremal disc, a disc of the largest radius determined by g, where genus g is the number of handles if S is orientable or the number of cross caps if S is non-orientable. In this talk we shall consider how many extremal discs are embedded in a compact non- orientable surface of genus 6. We know the answer for the non-orientable surfaces of genus g=3, 4, 5 and also g>6, so that g=6 is the final genus in our interest. By showing side-pairing patterns of the regular 30-gon, we present all non-orientable extremal surfaces of genus 6 admitting more than one extremal disc. We also determine the group of automorphisms for these surfaces.