Others have already suggested the right way of doing it but if you really want to use ternary operator you need to use parenthesis as:
$province = 7;
$Myprovince = (
($province == 6) ? "city-1" :
(($province == 7) ? "city-2" :
(($province == 8) ? "city-3" :
(($province == 30) ? "city-4" : "out of borders")))
);