Your allowance of a rowing technique with 〜させてもらいます
Grammar Explanation: Having someone do something with 〜てもらう

Akatsuki asks Akari for a gondola ride to his destination. Along the way, he asks whether he’ll make his deadline. Akari suggests Alicia should take over, but Akatsuki says he’s Akari’s customer (and paying the cheaper fare). Realizing her responsibility, Akari turns the gondola around so she can use her high-speed backward rowing. Alicia apologizes to Akatsuki for the turnaround.
- アリシア:
- 「今からお客様
( の視界( を遮( る漕( ぎ方( をさせてもらいます」- “From now on, she'll be using a rowing technique that blocks your view.”
- 暁
( : - 「むぅ?」
- “Mm?”
Key Points
〜させてもらいます = “we will be allowed to…”
Alicia frames the action as 漕
( ぎ方( をさせてもらいます: literally, “We will receive your allowing us to use this rowing method.”In context, it is a polite service-style announcement: “please allow us to…”
The action is the whole noun phrase before を
お客様
( の視界( を遮( る漕( ぎ方( means “a rowing method that blocks the customer’s view”.That entire phrase is the object of させてもらいます: Alicia is asking permission to use that specific rowing technique.