To find the product \((-2)(6)(-5)(-4)\), we can multiply the numbers step by step.
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First, multiply \(-2\) and \(6\): \[ -2 \times 6 = -12 \]
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Next, multiply \(-12\) by \(-5\): \[ -12 \times -5 = 60 \] (The product of two negative numbers is positive.)
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Finally, multiply \(60\) by \(-4\): \[ 60 \times -4 = -240 \]
So, the final product is: \[ \boxed{-240} \]