How do I generate combinations based on column values in SQL? (Is this even possible?)

How do I generate combinations based on column values in SQL? (Is this
even possible?)

I'm trying to make a new column in a table whose contents are based off
values of an existing pair of columns. Specifically if I have table
like(ID is not the primary key)
ID | Value | New Column(The column I want)
1 A A:apple
1 B A:orange
2 apple B:apple
2 orange B:orange
Im a novice to SQL, so any insight here would be really helpful.
Btw, Im using Oracle if that matters.
Additional Details: Im looking to pair Values:Values based on the fact
that their ID's dont match