Step 1 :Given the expression \(\left(6 x^{6}\right):\left(-3 x^{4}\right)\)
Step 2 :First, divide the coefficients of the two terms. The coefficient of the first term is 6 and the second term is -3. So, \(\frac{6}{-3} = -2\)
Step 3 :Next, subtract the exponents of the variables. The exponent of x in the first term is 6 and in the second term is 4. So, \(6 - 4 = 2\)
Step 4 :Therefore, the simplified form of the given expression is \(-2x^{2}\)
Step 5 :\(\boxed{-2x^{2}}\) is the final answer