|     A    |   B  | C | D  |  E  |      F       |
--|----------|------|---|----|-----|--------------|---
1 | 1,4,7,10 |  500 |   |  1 | 560 | (=500+60)    |
2 | 2,5,8,11 |  300 |   |  2 | 300 | (=300)       |
3 | 3,6,9,12 |  800 |   |  3 | 800 | (=800)       |
4 | 1,9      |   60 |   |  4 | 500 | (=500)       |
5 | 5,12     |   90 |   |  5 | 390 | (=300+90)    |
6 | 6,7,12   |   30 |   |  6 | 830 | (=800+30)    |
7 |          |      |   |  7 | 530 | (=500+30)    |
8 |          |      |   |  8 | 300 | (=300)       |
9 |          |      |   |  9 | 860 | (=800+60)    |
10|          |      |   | 10 | 500 | (=500)       |
11|          |      |   | 11 | 300 | (=300)       |
12|          |      |   | 12 | 920 | (=800+90+30) |
13|          |      |   |    |     |              |

As you can see in Column A the values in the cells are a string.
In Column D each number that appears in Column A is listed separately.
The idea is now to calculate the SUM in Column E whenever one of the numbers in Column D appears in a string in Column A.

Something like this:

=SUMIFS($B$1:$B$6,$A$1:$A$6,If number in cell D1 appears in one of the strings in Column A)

(Note: I only added Column F for a better explanation how the numbers in Column E are calculated)

Do you have any idea how to achieve this?