Assuming the digits_dialed field is at the top level of your JSON column (and that your column is JSON-typed), you can use this to get the ID of all the fields where digits_dialed is the string '2'.
Code:
WITH some_table(id, json_field) AS (
VALUES
(1::integer, '{"digits_dialed": "2"}'::json),
(2, '{"digits_dialed": "3"}'),
(3, '{"digits_dialed": "2"}')
)
SELECT
id,
json_field->>'digits_dialed' as digits_dialed
FROM some_table
WHERE json_field->>'digits_dialed' = '2';
Fiddle.
If digits_dialed is nested in a JSON object, you'll need #>> with e.g. (json_field#>>'{path,to,digits_dialed}') (
docs).