Those two goals are just notifications that you've started the timed portions of two long term, untimed goals. They will remain until you finish the entire first part of each quest. They don't have any requirements because they're just asking you to finish part one of each quest, if that makes sense?
You should have another goal for each quest further down in your book which will start you on your way with the actual goal tasks. For full details on what those goals are and what they require, you can check the threads I've linked below from the Main Story Goal Guide.
Misty Marshland goal line here.
Elemental Discovery goal line found here.
Hope this helps get you started.
Yes, you right, I have another goals at the bottom which are related with these ones.
Thank you a lot! Your information has been very helpful!