35 Grk “Asia”; in the NT this always refers to the Roman province of Asia, made up of about one-third of the west and southwest end of modern Asia Minor. Asia lay to the west of the region of Phrygia and Galatia. The words “the province of” are supplied to indicate to the modern reader that this does not refer to the continent of Asia. The expression all who lived in the province of Asia is good Semitic hyperbole (see Col 1:7, “all the world”). The message was now available to the region.
36 The word of the Lord is a technical expression in OT literature, often referring to a divine prophetic utterance (e.g., Gen 15:1, Isa 1:10, Jonah 1:1). In the NT it occurs 15 times: 3 times as ῥῆμα τοῦ κυρίου (rhēma tou kuriou; Luke 22:61, Acts 11:16, 1 Pet 1:25) and 12 times as λόγος τοῦ κυρίου (logos tou kuriou; here and in Acts 8:25; 13:44, 48, 49; 15:35, 36; 16:32; 19:20; 1 Thess 1:8, 4:15; 2 Thess 3:1). As in the OT, this phrase focuses on the prophetic nature and divine origin of what has been said.

In other versions

This continued for two years, so that all the residents of Asia heard the word of the Lord, both Jews and Greeks.

This went on for two years, so that all the Jews and Greeks who lived in the province of Asia heard the word of the Lord.

This went on for two years, so that all the residents of Asia, both Jews and Greeks, heard the word of the Lord.

This went on for the next two years, so that people throughout the province of Asia—both Jews and Greeks—heard the word of the Lord.

And this took place for two years, so that all who lived in Asia heard the word of the Lord, both Jews and Greeks.

And this continued by the space of two years; so that all they which dwelt in Asia heard the word of the Lord Jesus, both Jews and Greeks.

Public Domain