To determine the value of g(x), we need to understand the process of polynomial division and the relationship between the dividend (f(x)), the divisor (g(x)), the quotient (cx), and the remainder (d).

The Polynomial Division Process:
1. Dividend: f(x) = acx^3 + bcx + d
2. Divisor: g(x) = ? (to be determined)
3. Quotient: cx (given)
4. Remainder: d (given)

Key Points:
1. The degree of the quotient is always one less than the degree of the dividend. In this case, the degree of cx is 1, which means the degree of f(x) must be 2 (since it's a cubic polynomial).
2. The degree of the remainder is always less than the degree of the divisor. In this case, the remainder is a constant term (degree 0).

Now, let's consider the polynomial division process step-by-step:

Step 1: Divide the highest degree term of the dividend by the highest degree term of the divisor to determine the leading term of the quotient.
- The highest degree term of f(x) is acx^3, and we are given that the leading term of the quotient is cx. Therefore, acx^3 / ??? = cx.

Step 2: Multiply the divisor by the leading term of the quotient to obtain a product.
- We know that the leading term of the quotient is cx. Therefore, multiplying g(x) by cx gives us a product of c(cx) = c(cx^2).

Step 3: Subtract the product obtained in Step 2 from the dividend.
- Subtracting c(cx^2) from f(x) = acx^3 + bcx + d gives us a new dividend: acx^3 + bcx + d - c(cx^2).

Step 4: Repeat Steps 1-3 with the new dividend until the degree of the remainder is less than the degree of the divisor.
- Since the degree of the remainder is a constant term (degree 0), we can stop the division process here.

Conclusion:
Based on the given information and the steps of the polynomial division process, we can conclude that the value of g(x) is ax^2 + bd.