Go to the calendar view -> Format current view -> Apply formatting to Month -> Advanced mode -> Use following JSON codes.
{
"$schema": "https://developer.microsoft.com/json-schemas/sp/v2/calendar-formatting.schema.json",
"additionalEventClass": "=if([$Typeofrequest] == 'Vacation' && [$Region] == 'Northeast', 'sp-css-color-WhiteFont sp-css-backgroundColor-BgLightBlue sp-css-borderColor-PurpleText', if([$Typeofrequest] == 'Sick Day' && [$Region] == 'Northeast', 'sp-css-color-WhiteFont sp-css-backgroundColor-BgCoral sp-css-borderColor-PurpleText', if([$Typeofrequest] == 'Vacation' && [$Region] == 'West', 'sp-css-color-WhiteFont sp-css-backgroundColor-BgLightBlue sp-css-borderColor-GreenText','sp-css-color-WhiteFont sp-css-backgroundColor-BgCoral sp-css-borderColor-GreenText')))"
}
Result:
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