That looks like either a Norfolk Island Pine (Auracaria heterophylla) or a Cook Pine (Araucaria columnaris). It is not a pine, but a conifer from either Norfolk Island or New Caledonia in the Pacific. Both trees make very pretty landscape trees; unfortunately, the one pictured appears to have been topped, although I could very well be wrong about that. In the wild, both species tend to be slow growing, but can grow quite tall (150–200 feet). Keeping it in a pot should have dwarfed it a little, but it is already six-feet high, so not really suitable for your apartment...
- Norfolk Pines are popular house plants in the US because they like to grow in filtered sunlight or light shade, and can live in the low light intensity of most houses. Humidity and heated houses in the winter are issues (the plant tends to be very fussy), so I'm guessing that many die a year or two after purchase.
- Cook Pines are popular street trees in the tropical regions of the world. The tallest is about 150 feet high, living in a park in Brazil. They like full sun and a somewhat sheltered position (if in pots).
When young, both species look nearly identical, so it will be hard to tell them apart. It's important to know which tree it is, because Norfolk Island Pines do not like direct sun or very warm temperatures, while Cook Pines love full sun and do well in Hawaii and other tropical areas.
If the tree you pictured has always grown in its pot in full sun, then it's almost certainly a Cook Pine. In that case, it would grow just fine on your terrace, provided that the area is sheltered from strong winds.