The phrase "acknowledgement of how" is correct and usable in written English.
It can be used when discussing the recognition or acceptance of a particular way or method of doing something.
Example: "The acknowledgement of how the team approached the project was crucial for its success."
Alternatives: "recognition of how" or "acceptance of how".
Palin might be a kind of acknowledgement of how badly the Bush years had turned out.
The trials represented a formal acknowledgement of how pervasive the mafia was in Sicily.
The surroundings are appropriate, for this is not just a show but an acknowledgement of how her sense of style opened the minds of her peers.
But while these facts are well documented and constantly discussed, there is less acknowledgement of how the episode has affected Sikhs since.
The announcement was low-key with the singer not mentioning it in her own social media posting about Utopia, perhaps in acknowledgement of how widespread the digital currencies are becoming.
But while STS is now well understood in many helping professions, there is a dearth of research, understanding, or acknowledgement of how it affects educators, according to Stephen P. Hydon, a clinical professor at the University of Southern California.
President Kennedy followed his moonshot goal with acknowledgements of how difficult the task would be.
In acknowledgement of just how well it worked, given even more powerful dimensions by the ideal acoustics, she smiled warmly at her choir and her smiles were returned.
It's also a tacit acknowledgement of just how crowded services-for-services has become (and yes the ouroboros of the absurdity contained in the previous statement isn't lost on me).
It's an acknowledgement of just how far behind they are, when the consultants are willing to show Romney attempting to look sincere.
Acknowledgement of Gifts instructs how to generate official gift receipts and thank you letters.
