How to fix UnboundLocalError

[Gribouillis]

would you recommend a different method of keeping track of the answers_right, without resorting to a global variable?

You are reaching the point where you have functions that manipulate external data and you need a way to manage both the data and the function. That's why classes were invented. Here is how you can code this by using a class:

class BoneFinder:
    foot_bones = [
        "calcaneus", "talus", "cuboid",
        "navicular", "lateral cuneiform",
        "intermediate cuneiform", "medial cuneiform",
    ]

    def __init__(self):
        self.answers_right = 0
 
    def examine(self, bone_name):
        if bone_name.lower() in self.foot_bones:
            print("correct!")
            self.answers_right += + 1
        else:
            print("incorrect")

finder = BoneFinder()         
finder.examine(input("enter name of a bone: "))
finder.examine(input("enter name of another bone: "))
 
print("number of foot bones correctly identified: ", finder.answers_right)

In this code, a single entity holds the variable answer_right between subsequent calls. The code looks more complicated than your program but in fact, it is easier to extend by adding new features.