Important Distinction

Percent is relative to what you're talking about, and this is probably why you are getting different answers based on the order you're doing things.

Percentage Points are absolute and order is only going to change whether it's positive or negative. Generally you use the later date first so that an increase between two years gives a positive value.

Find the Percentage Points first.

Given:
    A1 = 1/6
    A2 = 4/10

Find difference in A1 -> A2:
    ΔA = A2 - A1
    ΔA = 4/10 - 1/6
*   ΔA = 7/30 
*   ΔA = 23.3..%

So A had an increase in 7/30 or 23.3% Percentage Points.

If you want to know impact in Percentage Points, then that's your answer for A.

A contributed 7/30 or 23.3% to the total change between those years. Remember though, this is Percentage Points, not Percent.

If you want your impact relative to the change in the total percent, then the total percent is going to be your denominator. Keep in mind the distinction here between Percent and Percentage Points ... now we're finding a Percent relative to the total change.

In theory, the numbers from A, B, and C should all add up to 100%, but because we're dealing with both increasing and decreasing values, you're going to get non-intuitive values like negative percents or percents greater than 100.

Given:
    ΔA = 7/30
    T1 = 12/30
    T2 = 7/20

Find difference in T1 -> T2
    ΔT = T2 - T1
    ΔT = 7/20 - 12/30
*   ΔT = -1/20
*   ΔT = -5%

Determine the percent impact A1->A2 had on T1->T2
    AI% = ΔA / ΔT
    AI% = (7/30) / (-1/20)
*   AI% = -14/3
*   AI% = -466.7..%

The change in A actually contributed -14/3 or -466.7% of the total change over the two years. Since this is a negative value, this means it worked against the total change.

Something else we might want to help us word our answer is the actual percent change in both the total and A instead of the Percentage Point changes.

Given:
    T1 = 12/30
    T2 = 7/20

Determine the percent change in T1->T2
    T% = 1 - T2 / T1
    T% = 1 - (12/30) / (7/20)
*   T% = -1/7
*   T% = -14.3..%

So the total changed by -14.3..% relative to the earlier year.

Given:
    A1 = 1/6
    A2 = 4/10

Determine the percent change in A1->A2
    A% = 1 - A2 / A1
    A% = 1 - (1/6) / (4/10)
*   A% = 7/12
*   A% = 58.3..%

So A changed by 58.3% relative to the earlier year.

So now we have all the information to word the impact relative to the first year based on both Percentage and Percentage Points,

For an answer in Percentage we can say

The total change between the two years was -14.3%. Product A had an increase of 58.3% which had an impact of -466.7% on the total change.

A proper way to word the answer in Percentage Points would be

The total change between the two years was -5 percentage points, with Product A contributing 23.3 percentage points.

A more ambiguous but annoyingly common way to word it would be

The total change between the two years was -5%, with Product A contributing 23.3%.

The reason this last one is more ambiguous is you don't know if those are Percents or Percentage Points, especially if you're going to use both in the same answer.

** If we wanted a mixed answer, we could say

The total change between the two years was -5 percentage points. Product A had a change of 23.3 percentage points with a resulting impact of -466.7% on the total.

A very bad way to word your answer would be

The total change between the two years was -5%. The impact of Product A was -466.7%.

This is bad because you are mixing percents and percentage points with no clear distinction of which is which.

In my opinion, the best answer would be the one I put stars next to.