Which form is to be preferred?
- I would like to ask you a favour.
- I would like to ask you for a favour.
According to this Google NGram, all of the following forms are in use:
As you can see, the forms without the preposition for are more common (with "ask you a favor" generating the highest results). In common use, one may conclude that this is the preferred form.
I would say the former is preferred/more common in colloquial/spoken English. The latter is not incorrect but used less often.
Compare it with "Asking a lunch" and "Asking for a lunch" Here, "lunch" is not the actual thing which is being asked; and that's why it should be "Asking for a lunch"
But in case of favour, it's the "favour" which is directly being asked.
Similarly, you can also compare 1. Asking a date 2. Asking for a date
So the correct usage is: "I would like to ask you a favour"
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