Kyle asked no, he begged me to switch hours with him at work so that he could attend abigail's party.

The answer is: Kyle asked me, no, he begged for me to switch hours with him at work so that he could attend Abigail's party.

The verb ask is transitive, which means its meaning sounds incomplete if an object is not mentioned. From the context we can infer that the object pronoun would best fill in the blank, since it is used on the second part of the sentence after the verb "beg".

The verb beg is also transitive and, in the sentence above, it seems to require the preposition to help complete it meaning. The object of the verb is the structure "me to switch hours etc."

Both verbs, ask and beg, usually demand two objects (direct and indirect):

ask for / ask to do

beg for

If the structure was in a formal context, "begged me to switch etc." would also be acceptable.

my guy how are we supposed to know

might need to ask questions people no or have read somthing about.