Acts of the Apostles 13:48 (NASB)
When the Gentiles heard this, they began rejoicing and glorifying the word of [fn]the Lord; and all who had been appointed to eternal life believed.
The Greek word translated "appointed" in the OP version of the verse, refers to an agreement by mutual consent. Since another Greek word (also translated as "appointed" refers to a unilateral assignment, some claim it was God who had "appointed" them unilaterally. Utter nonsense.
They had received direction from Paul as to the Good News, and as many as agreed with and took that direction for eternal life, believed. Here is an alternate translation choice which suggest mutual consent.
TLB
When the Gentiles heard this, they were very glad and rejoiced in Paul’s message; and as many as wanted eternal life, believed.
The Greek word, transliterated "tasso" is in the passive voice, indicating the arrangement has been established by someone other than the person accepting the arrangement. For example say someone is "placed" under authority and then gives direction to others. He has accepted the arrangement established by another. See Luke 7:8
Romans 13:1 teaches that the governing authorities have been "established" by God, but note they are governing which shows their agreement with the arrangement.
In Acts 22:10 Paul is sent to Damascus, as he has agreed to do what the Lord has arranged.
In all the "passive" arrangements the participant agrees with direction given and participates.
When the Gentiles heard this, they began rejoicing and glorifying the word of [fn]the Lord; and all who had been appointed to eternal life believed.
They had received direction from Paul as to the Good News, and as many as agreed with and took that direction for eternal life, believed. Here is an alternate translation choice which suggest mutual consent.
TLB
When the Gentiles heard this, they were very glad and rejoiced in Paul’s message; and as many as wanted eternal life, believed.
Romans 13:1 teaches that the governing authorities have been "established" by God, but note they are governing which shows their agreement with the arrangement.
In Acts 22:10 Paul is sent to Damascus, as he has agreed to do what the Lord has arranged.
In all the "passive" arrangements the participant agrees with direction given and participates.