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Hey there :) 
You are allowed to sell your game using the assets and you can distribute it yourself.
The last part just means: You can't tell in the credits that you made the assets by yourself, that's all.

Hope that answers the questions, if anything else, let me know.
regards,

Sam

Thank you so much. One more question. Don't know if you'd know this, but can I combine several asset packs from different authors in one game? In this scenario, all the asset packs are allowed for commercial use.

usually, Yes. 
as for my Assets, you can do this. However there may be other assets on itch which will not allow this. (But I can’t Imagine why some would forbit that)

Thanks again!