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The phrase "accepts this assignment" is correct and usable in written English.
You can use it when referring to someone agreeing to take on a specific task or responsibility.
Example: "After reviewing the project details, she gladly accepts this assignment and is ready to begin work."
Alternatives: "takes on this task" or "agrees to this assignment."
Similar(59)
BlackRock said it hadn't made a decision on whether to accept this assignment.
Realizing my credibility would forever be challenged at the Book Review office, I accepted this assignment — if only to set the record straight.
"When I accepted this assignment, I said that I intended to conduct an investigation that is objective, thorough and fair," Mitchell said.
You can "take the coward's strategy and say, 'I intend to accept this assignment and I'm very excited, but I wonder if there's any wiggle room with the fee,' " Mr. Cohen said.
However, I am very pleased that he has accepted this assignment.
A grizzled LA detective is brought in to show the local cops how to take down a villain this scary - a detective who has accepted this godforsaken assignment because he is in trouble with the Internal Affairs department back in the big city.
When Mr. Villazón, in the midst of a vocal crisis, pulled out last spring, the young Maltese tenor Joseph Calleja, who had never sung this daunting role, accepted the assignment.
I wouldn't have accepted the assignment if I hadn't seen this video on MTV.
While the Nets periodically double-teamed him, Martin eagerly accepted the assignment Nets Coach Byron Scott asked of him this morning.
Mr. Olbinski accepted the assignment at once.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com