I understand how the question arrived at the conditional probabilities, however couldn't the question also be interpreted this way?
Since the question never stated that the 2 dice were different, what if we assume they were not distinct and also we can assume that the 2 dice is thrown at the same time, thus
Now to have a sum of 4 and a max of 3, all we need is to roll a 1 and a 3, there is no order here since we are throwing the dice at the same time and the dice are NOT distinct. Thus the numerator becomes 1/6 * 1/6
To get a maximum of 3, all we need is to roll a 1 and a 3 or 2 and a 3 or 3 and a 3 (again there is no order since we are throwing the dice at the same time)
Thus the denominator is 3*(1/6 * 1/6)
Would the above also be a valid interpretation?