Was it truly done from a subclavian approach, or was it a femoral approach with selective catheter placement into the subclavian and right internal carotid?
Assuming this was done from a femoral approach and patient has normal anatomy (not bovine arch), for the cath placements, you have:
36217 (Right internal carotid, if CATH was placed - always code to the highest order within a vascular family)
36218 (Right subclavian)
If access was from the subclavian, then you just have 36216 for the right internal carotid catheterization, as the subclavian is non-selective.
I'm not sure I would code 75676 unless the physician documents specific findings for the common carotid artery. I also wouldn't code 75710 if the intent of injecting in the subclavian was to view the vertebral - that is captured in 75685.
If you have a full copy of the report you can post, it would better help us determine the correct coding for this case. Placing a wire in the internal carotid artery doesn't necessary constitute selective catheterization unless he actually placed a catheter there and took images.