task handing or task processing?
How to describe that you are capable of doing things well, especially you are capable of completing tasks that ought to be completed by more than one people. ?

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Both are awkward and I would not advise  you to use either.  Why don't you give us the complete paragraph so that we can properly judge how you should write it?  Just throwing two phrases around out of context is not helpful to you or anyone else.

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Also, multi-tasking means you can do more than one task at a time.  Many people use this term on a resume for employment.

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It should be task-handling.