Final answer:
Without given marginal utilities, we must use the budget constraint to find which options are viable. Only option d (1 unit of A, 6 units of B, 1 unit of C) does not exceed the $12 budget, making it the only possible utility-maximizing choice provided.
Step-by-step explanation:
To determine how many units of each good a consumer should buy to maximize utility with a $12 budget, we can apply the concept of consumer equilibrium. This concept states that a consumer maximizes utility when the ratios of the marginal utility to price for all goods are equal. We do not have the actual utilities given in the problem, so we must evaluate the options provided by calculating the total cost for each combination and ensuring it does not exceed the budget constraint.
Option a, we calculate 2 units of A ($4) + 4 units of B ($4) + 2 units of C ($6) = $14, which exceeds the $12 budget. Option b is 3 units of A ($6) + 2 units of B ($2) + 2 units of C ($6) = $14, also over the budget. For option c, 4 units of A ($8) + 2 units of B ($2) + 1 unit of C ($3) = $13, again over the budget. And option d, which is 1 unit of A ($2) + 6 units of B ($6) + 1 unit of C ($3) = $11, is within the budget.
Only option d falls within the $12 budget so it would be the choice that a utility-maximizing consumer could actually afford. However, to truly determine the utility-maximization, we would need additional information on the marginal utilities of each good. But based on the information provided and the budget constraint, option d is the only feasible choice.