The word "egalize" is not a commonly used term in English, and it is not found in most dictionaries. However, based on its pronunciation, it appears to be a variation of the word "legalize." In IPA phonetic transcription, the word would be spelled /ɪˈɡal.aɪz/, with the stress on the second syllable. This indicates that the first syllable is pronounced with a short "i" sound and the second syllable has a long "a" sound. The final syllable is pronounced with a "z" sound.
The word "egalize" does not have an established etymology; it appears to be a neologism or a coined word. It is likely a combination of "equal" or "equality" and the suffix "-ize", which is used to form verbs denoting the process of making something or someone equal or egalitarian.