"Η ζώνη μου."

[Lng52-._]

Is it pronounced like: "zhoni" or "zoni"?

[mizinamo]

Yes :)

Because Greek has no "sh" or "zh" sounds, the "s" and "z" sounds can move a bit in that direction without causing a possible confusion between words. So Greek "s, z" sometimes sounds a bit like "sh, zh". (Though I think the sound never moves all the way to a typical English "sh, zh" sound, just somewhere in between.)

For a learner, I'd recommend using English "s, z" rather than try to imitate the in-between sounds that you might hear from Greeks.

[Dimitra956826]

It's almost the same thing, as soon as the h is silent. ^.^

[mizinamo]

I think with "zh" is meant the sound of "j" in French "journal", or English "s" in "measure".

[Joridiy]

It sounds rather to the Polish «rz» and «sz»

[DemiVandeH]

I said my belt?

[Dan_Silhavy]

Why is there capital "Z"?

[D_..]

It's not the capital form, ζ is how the small Ζ is written in Greek.