In colloquial English, this is also rendered as "How are those new banks?"
Why is the definite article used here? Is 'Milyenek azok uj bankok' also correct? I can't imagine an equivalent in english where we use "those" with an article.
In English we don't, but in Hungarian we always do. The words for this / that / these / those are always joined to their noun with a definite article.
a bank - the bank
az a bank - that bank
ez a bank - this bank
azok az új bankok - those new banks
ezek a csunya szovjet bankok - these ugly soviet banks
and so on.