To evaluate the expression \(6a + 4b - 3c\) for \(a = 3\), \(b = 5\), and \(c = 10\), substitute the values of \(a\), \(b\), and \(c\) into the expression.
\[ 6a + 4b - 3c = 6(3) + 4(5) - 3(10) \]
Calculating each term:
\[ 6(3) = 18 \]
\[ 4(5) = 20 \]
\[ 3(10) = 30 \]
Now substitute these results back into the expression:
\[ 18 + 20 - 30 \]
Now perform the addition and subtraction:
\[ 18 + 20 = 38 \]
\[ 38 - 30 = 8 \]
Thus, the value of the expression is \(\boxed{8}\).