Final answer:
The right superior oblique muscle (RSO) is affected if a patient has a right hyperdeviation that worsens in right gaze and with left head tilt, which is consistent with the details provided in the Parks 3 Step Test.
Step-by-step explanation:
The Parks 3 Step Test is used to identify the affected extraocular muscle in cases of vertical diplopia (double vision). If a patient has a right hyperdeviation that is worse in right gaze and left head tilt, the muscle likely to be affected according to the test would be the right superior oblique (RSO), represented by option C. The superior oblique muscle aids in intorsion (medial rotation of the eye around its axis), depression, and abduction of the eye. Hence, if a patient has difficulty tilting their head to the left and the problem is exacerbated in right gaze, it suggests a dysfunction of the muscle responsible for those movements, which in this case is the right superior oblique muscle.