Is H a Normal Subgroup If Every Left Coset Equals a Right Coset?

[nbacombi]

Let G be a group and H be a subgroup of G. If every left coset xH, where x in G, is equal to a right coset Hy, for some y in G, prove H is normal subgroup.

Help?

 

[lanedance]

so what is the definition of normal subgroup?