Trail and Error!

Algebra Level pending

For a function $$f(x)$$,

$$f(1) - f(-1) = 6\\f(2) - f(-2) = 3\\f(3) - f(-3) = 2\\f(6) - f(-6) = 1$$

If the above information holds true, and $$f(x) - f(-x)$$ follows same pattern for all values of $$x$$, find the value of $$f(12) - f(-12)$$

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