Γεια σου Ιάκοβε
The pronunciation of φεγγάρι is between fegari and fengari. Actually it is closer to fegari. As for the spelling φενγάρι, it is completely wrong.
The double consonant γγ is usually pronounced as ng when it comes from the combination of the preposition εν and the letter γ.
Example:
έγγαμος < εν + γάμος (engamos) = married
εγγραφή < εν + γραφή (engrafi) = registration
In other cases pronunciation could be either g or ng, depending on the word and the area of Greece you may be.
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.