Find the product of the functions \(f(x) = 3x^2 + 2x + 1\) and \(g(x) = 2x^2 + 3x + 4\).

Step 1 ：First, we need to distribute each term of the first function to each term of the second function.

Step 2 ：Distribute \(3x^2\) in \(f(x)\) to each term in \(g(x)\), we get \(6x^4 + 9x^3 + 12x^2\).

Step 3 ：Distribute \(2x\) in \(f(x)\) to each term in \(g(x)\), we get \(4x^3 + 6x^2 + 8x\).

Step 4 ：Distribute \(1\) in \(f(x)\) to each term in \(g(x)\), we get \(2x^2 + 3x + 4\).

Step 5 ：Add all the terms together, we get \(6x^4 + 9x^3 + 12x^2 + 4x^3 + 6x^2 + 8x + 2x^2 + 3x + 4\).

Step 6 ：After combining like terms, we get \(6x^4 + 13x^3 + 20x^2 + 11x + 4\).