A) The parliament accepts the change by a simple majority vote, and the change will "rest" until the next election. After the election, the change will pass with a 2/3 majority vote by the new parliament.
B) The parliament deems that the change is urgent by at least a 5/6 majority vote. Then the change will be voted upon and will pass with a 2/3 majority vote.
Finland is not “changing the constitution“. Not yet, at least. Such a change has been _proposed_ by a group appointed by the ministry of justice, and is now being _discussed_ in public. None of the above steps to actually change the constitution has taken place yet. I find it unlikely that a 2/3 majority vote for a change like this can be achieved with the currently elected parliament.
The annoying thing I find about the news coverage about this is that they make it sound like it's already decided. We're seeing headlines to the tune of ”here are the new wiretap rights for Finnish Security Service”. It is not decided yet.