Priority for different bonds and functional groups

[Huanyu Nie 2A]

If a compound has both triple bond and double bond, which one should have priority for numbering? On page 50 of the orange textbook, the upper right molecule contains a double and a triple bond and the double has a lower number. I'm confused if the rule is affected by the halogenated groups.

[Neel Patel - 2A]

There is a chart that shows the priority of different bonds and functional groups