The `e’ in the first syllable and the `y’ in the final syllable are like `i’ in `hit’, `bit’, and `pit’. The `gem’ in the second is pronounced like the word `gem’. The `o’ is like the `a’ in `china’ and the main stress is on the second syllable. This is one way of pronouncing the word.
`Hegemony’ is a formal word and is used to refer to a situation in which one group has more control or power than others.