Darby is on a deserted island and wishes to make an \(X\) on the beach using \(6\) brown coconuts, \(9\) green coconuts, her red shoe, and a white frisbee. If each stroke of the \(X\) has \(9\) objects with one overlap in the center, in how many different ways can this be done?

\(\)

**Details and Assumptions:**

- The \(X\) has strokes which meet at a right angle, so that when viewed correctly it also looks like a plus sign (\(+\)).
- Two configurations are distinct if they cannot be obtained through rotation.

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