To factor the expression \(-4x^3 + 6\) completely, we can start by factoring out the greatest common factor (GCF) from both terms.
The GCF of \(-4x^3\) and \(6\) is \(2\):
\[ -4x^3 + 6 = -2(2x^3 - 3) \]
Now we check if \(2x^3 - 3\) can be factored further. This expression is in the form of a difference of cubes, but it does not fit that form exactly since it lacks a perfect cube.
Since \(2x^3 - 3\) is not factorable further using real coefficients, the fully factored expression is:
\[ \boxed{-2(2x^3 - 3)} \]
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