To evaluate the expression \(\frac{stu}{s - u}\) with the values \(s = -10\), \(t = 0\), and \(u = 12\), we follow these steps:
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Calculate \(stu\): \[ stu = (-10)(0)(12) = 0 \]
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Calculate \(s - u\): \[ s - u = -10 - 12 = -22 \]
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Now substitute these values into the expression: \[ \frac{stu}{s - u} = \frac{0}{-22} \]
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Simplifying this, we find: \[ \frac{0}{-22} = 0 \]
Thus, the value of the expression is \(\boxed{0}\).