This problem may sound difficult at first since it deals with two figures (a circle and an intersecting line) and asks for a maximum value. However, it's really testing a single geometric concept — the greatest distance between two points on a circle is equal to the diameter, or twice the radius. This is suggested by the key phrase "maximum possible distance".
If you realized at once that you were looking for the diameter you probably didn't bother with a sketch, since the diameter is just twice the radius of 4. But, if you didn't, drawing a quick diagram like this:
would help you to visualize that the maximum distance would be the circle's diameter, which would then lead you to the correct answer of 8:
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