What I understand from the question is we have to define goals for facebook notification feature and not actually list out the metrics.
The defined goals always need to be quantitative, that would tell us whether the feature that we released is doing well or not. If we are not able to achieve those quantitative goals, it’s time to think, if there's a problem with the feature, or if we really need the feature at all.
Let’s list out types of notifications sent by Facebook.
Direct Message notifications
Like my page notification
Fb events invite notification
Like, Tag and comment notification ( Photo, Post )
Let’s take the “Direct message notification” and try to define a goal for the same .
Direct Message notifications - users interact with messages in 3 ways ,
Sliding down the notification and reading the message
Clicking on the notification , reading the message and closing the app
Clicking on the notification , reading the message and replying to the message.
If we follow the HEART framework , where T stands for task success,
All 3 of these can be considered as Task Success for this particular feature.
Hence, In the case of “Direct message notifications” our goal is Task success.
Now , a quantitative and measurable goal would be that,
75% of the users should interact with “Direct Message notifications” in one of the above-mentioned ways.