Find the product. Simplify your answer. \[ (2 c-1)(4 c+2) \]

To find the product of \( (2c - 1)(4c + 2) \), we can use the distributive property, also known as the FOIL method for binomials. First, multiply the first terms: \[ 2c \cdot 4c = 8c^2. \] Next, multiply the outer terms: \[ 2c \cdot 2 = 4c. \] Then, multiply the inner terms: \[ -1 \cdot 4c = -4c. \] Finally, multiply the last terms: \[ -1 \cdot 2 = -2. \] Now, combine all these results: \[ 8c^2 + 4c - 4c - 2. \] Notice that the \( 4c \) and \( -4c \) cancel each other out. Thus, the expression simplifies to: \[ 8c^2 - 2. \] So, the final answer is: \[ \boxed{8c^2 - 2}. \]