Using the value of a JSON object that is stored in a PostgreSQL JSON array
You can use json_array_elements to turn a JSON array into a rowset:

SELECT  "ID" as JobId
,       t-&gt;&gt;'id' as TaskId
FROM    Table1 j
CROSS JOIN
        json_array_elements("Details"-&gt;'tasks') t
WHERE   cast(t-&gt;&gt;'due_on' as date) = '2015-06-08';


The cast(... as date) works around the 2015-06-8 date which misses a leading 0 before the day.  If your format is always YYYYMMDD, you can omit the cast.