Revered Members,
In the case of two parallel current carrying conductors placed at a distance 'x' apart, the force is attractive if the current flows in the same direction in both the conductors and its repulsive when current flows in opposite direction. How the direction of current determines if the force is repulsive or attractive?

 

The field is circular around a conductor and would have a direction of clockwise or counter clockwise. Magnets attract opposite poles.

two clocks next to each other.

The pole is the arrow of direction of movement.
The head of the arrow will be North is this example.

The arrow around both conductors points to the right.

The arrow around the left conductor will point at the tail of the arrow around the right conductor.

The 'magnets' are showing opposite poles to each other and the wires are pulled together.

 

The field is circular around a conductor and would have a direction of clockwise or counter clockwise. Magnets attract opposite poles.

two clocks next to each other.

The pole is the arrow of direction of movement.
The head of the arrow will be North is this example.

The arrow around both conductors points to the right.

The arrow around the left conductor will point at the tail of the arrow around the right conductor.

The 'magnets' are showing opposite poles to each other and the wires are pulled together.

Interesting question, and I really like your explanation but....

What you say holds true when both clocks are at 12 O'Clock and 6 O'Clock.

What about when the left hand clock is at 3 O'Clock and the right hand clock is at 9 O'Clock ? (the mid point between the two wires). Won't repulsion occur?

Does the 12 and 6 "opposites attract" effect over-power the 3 and 9 repulsion effect?

... or do I completely misunderstand?

I know you are right, but I struggle to understand the details.

EDIT: I think I found the answer for myself here:

http://webphysics.davidson.edu/physlet_resources/bu_semester2/c14_forcewires.html

And I think my guess was right

 

If we try using the magnetic and electric circuit analogy

the magnetic field will try to establish itself along the path of least resistance. (reluctance I believe is the proper analogous unit)

So the point of 3 o'clock and 9 o'clock on the conductors(between them) would represent a zone with a very high resistance to the formation of the magnetic field due to the conflicting directions of field orientation there. While on the opposite sides, or the outer edges of the conductors the field direction is the same as it is for a single conductor. This establishes the path around the outside of the two conductors as the path of least resistance and the magnetic force is concentrated there.

The result is the forcing together of the conductors due to magnetic attraction. The attraction is the result of the field assuming its most compact form, and also, the shortest route that closes back upon itself (a circle in this case) and dragging the conductor from which it emenates along with it. With two conductors magnetic fields trying to assume the same path, the conductors themselves also try to occupy the same physical space, to make it possible. We call it attraction.

 

@Kermit2

Another impressive explanation, which solves the mystery for me. Many thanks.

Hope it benefits the OP too