2:19a So Bathsheba went to King Solomon to speak to him for Adonijah.

Bathsheba went to King Solomon in order to speak to him for Adonijah.
-or-
Bathsheba went to tell King Solomon what Adonijah had requested.

2:19b The king stood up to greet her, bowed to her, and sat down on his throne.

The king rose ⌊from his throne⌋ to meet her and bowed to her. Then he sat down on his throne ⌊again⌋.
-or-
The king stood up to greet her. He bowed to her ⌊politely/respectfully⌋ before taking his seat on the great/royal throne/seat ⌊again⌋.

2:19c Then the king had a throne brought for his mother,

He had ⌊his men⌋ bring another throne for his mother ⌊and place it on his right⌋.
-or-
He told ⌊his servants⌋ to bring ⌊another⌋ great/royal seat/throne
-or-
He ordered his servants, “Bring (plur) a throne for the mother of the king!”

2:19d who sat down at his right hand.

Bathsheba then sat there.
-or-
so that his mother could sit ⌊in honor⌋ at his right side.
-or-

⌊They placed/set it⌋ at his right hand side, and Bathsheba sat down in the/that ⌊place of honor⌋.

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