Acts 21:40, 22:2
⁴⁰And after he gave him permission, Paul stood on the steps, and motioned to the people downward with his hand.  And when it was largely quiet, he addressed them in the Hebrew language, and said…
²And when they heard him addressing them in the Hebrew language, they offered greater silence.

Here I am focusing on the progression from “when it was largely quiet” in 21:40 to “they offered greater silence” in 22:2.

πολλῆς δὲ σιγῆς γενομένης προσεφώνησεν τῇ Ἑβραΐδι διαλέκτῳ λέγων
largely and quiet became, he addresed in the Hebrew language, saying

Ἀκούσαντες δὲ ὅτι τῇ Ἑβραΐδι διαλέκτῳ προσεφώνει αὐτοῖς μᾶλλον παρέσχον ἡσυχίαν.
when they heard and that in the Hebrew language he addressed them greater they offered a silence.

Starting with Wycliffe and Tyndale, they interpreted πολλῆς as an adjective rather than the adverb it is in this context.  And most all of the translations tells us that the mob became very silent merely because Paul motioned with his hand. Really, the mob that was just trying to kill him?

Wycliffe
Poul stood in the grees, and bikenede with the hoond to the puple. And whanne a greet silence was maad, he spak in Ebrew tunge, and seide,
And whanne sum herden that in Ebrew tunge he spak to hem, thei yauen the more silence.

Tyndale
Paul stode on ye steppes and beckned with the honde vuto the people and ther was made a greate silence.
Whe they hearde that he spake in ye Ebrue tonge to them they kept the moore silence.

Some translations do not even translate the word πολλῆς:

God’s Word
So Paul stood on the stairs of the barracks and motioned with his hand for the people to be quiet. When the mob was silent, Paul spoke to them in the Hebrew language.
When the mob heard him speak to them in Hebrew, they became even more quiet.

Good News Bible
so Paul stood on the steps and motioned with his hand for the people to be silent. When they were quiet, Paul spoke to them in Hebrew:
When they heard him speaking to them in Hebrew, they became even quieter;

CEV
so Paul stood on the steps and motioned to the people. When they were quiet, he spoke to them in Aramaic:
When the crowd heard Paul speak to them in Aramaic, they became even quieter.

Many translations that do translate πολλῆς end up contradicting themselves, such as the NLT.  Verse 31 says there was “a deep silence” but then in v. 2 it says “the silence was even greater.”
How can you have a silence greater than “a deep silence”?  And there is no word for “even” in the Greek.

New Living Translation

so Paul stood on the stairs and motioned to the people to be quiet. Soon a deep silence enveloped the crowd, and he addressed them in their own language, Aramaic.
When they heard him speaking in their own language, the silence was even greater.

Now I will focus on the word παρέσχον in 22:2, which is 3rd person plural, they, they were offering.  The NLT does not correctly render that “they” part, see above.  But most translations do not correctly render the verb as “offered, afforded, gave” to someone.  Instead, they say something like “became” or “were”:

KJV
Paul stood on the stairs, and beckoned with the hand unto the people. And when there was made a great silence, he spake unto them in the Hebrew tongue, saying,
And when they heard that he spake in the Hebrew tongue to them, they kept the more silence:

NKJV
Paul stood on the stairs and motioned with his hand to the people. And when there was a great silence, he spoke to them in the Hebrew language, saying,
And when they heard that he spoke to them in the Hebrew language, they kept all the more silent.

TNIV
Paul stood on the steps and motioned to the crowd. When they were all silent, he said to them in Aramaic
When they heard him speak to them in Aramaic, they became very quiet.

CSB

Paul stood on the steps and motioned with his hand to the people. When there was a great hush, he addressed them in Aramaic:
When they heard that he was addressing them in Aramaic, they became even quieter

ESV
Paul, standing on the steps, motioned with his hand to the people. And when there was a great hush, he addressed them in the Hebrew language, saying:
And when they heard that he was addressing them in the Hebrew language, they became even more quiet.

NABRE
Paul stood on the steps and motioned with his hand to the people; and when all was quiet he addressed them in Hebrew.
When they heard him addressing them in Hebrew they became all the more quiet.

NASB
Paul, standing on the stairs, motioned to the people with his hand; and when there was a great hush, he spoke to them in the Hebrew dialect, saying,
And when they heard that he was addressing them in the Hebrew dialect, they became even more quiet; and he *said,

NET
Paul stood on the steps and gestured to the people with his hand. When they had become silent, he addressed them in Aramaic,
(When they heard that he was addressing them in Aramaic, they became even quieter.)

NRSV
Paul stood on the steps and motioned to the people for silence; and when there was a great hush, he addressed them in the Hebrew language, saying:
When they heard him addressing them in Hebrew, they became even more quiet.

Here is how it should be translated:

DRP
Paul stood on the steps, and he motioned to the people downward with his hand.  And when it was largely quiet, he addressed them in the Hebrew language, and said,
And when they heard him addressing them in the Hebrew language, they offered greater silence. You can download the DRP translation here .