2:22a King Solomon answered his mother,

King Solomon replied to his mother,
-or-
But King Solomon responded,
-or-
But King Solomon replied that

2:22b “Why do you request Abishag the Shunammite for Adonijah?

“Why are you (sing) asking for Adonijah to get/receive Abishag from Shunem as his wife?
-or-
“What! Let ⌊my older brother⌋ Adonijah marry Abishag?
-or-

⌊he was shocked/angry⌋ that she should ask for Adonijah to be allowed to marry Abishag.

2:22c Since he is my older brother,

He is my older brother!
-or-
He is older than I ⌊and wants/expects that⌋.
-or-
He was older than Solomon,

2:22d you might as well request the kingdom for him

It seems/appears that you (sing) want him to get/receive the kingdom/kingship ⌊as well⌋ !
-or-
That is like asking for him to become king,
-or-
so it implied/indicated that she wanted Adonijah to become the king,

2:22c-d (reordered)

He is my older brother, so it is the same as asking if I would give him the kingdom!

2:22e and for Abiathar the priest and for Joab son of Zeruiah!”

Yes, let him ⌊gain/benefit,⌋ and the priest Abiathar and Zeruiah’s son Joab also!”
-or-
He would ⌊rule Israel⌋, and with him would be the priest Abiathar and Joab the son of Zeruiah.”
-or-
Then he and Abiathar the priest and Joab the son of Zeruiah would all be ⌊powerful/content⌋.

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