Divide. \[ \frac{4 x^{3}-2 x^{2}-6}{2 x+1} \]

Step 1 ：Divide the first term in the numerator by the first term in the denominator. This will give us the first term of the result.

Step 2 ：Then, multiply the denominator by the first term of the result and subtract it from the numerator.

Step 3 ：Repeat this process until we can't subtract anymore.

Step 4 ：The result of the division is a tuple where the first element is the quotient and the second element is the remainder.

Step 5 ：So, the division of the given polynomials results in a quotient of \(2x^2 - 2x + 1\) and a remainder of \(-7\).

Step 6 ：Final Answer: The result of the division is \(\boxed{2x^2 - 2x + 1}\) with a remainder of \(\boxed{-7}\).