Note that rectangles, squares, parallelograms and triangles are 1, 2, 3 and 4 respectively.

If the first line 1234 is fixed, then if the second line and the third line are selected, only the fourth line is determined.

In order to avoid duplication, for any line, when the position of 1 is selected, 2, 3 and 4 are arranged in turn.

Then the arrangement under the conditions is:

1234 1234 1234 1234 1234 1234

4 123 4 123 34 12 34 12 234 1 234 1

34 12 234 1 4 123 234 1 4 123 34 12

234 1 34 12 234 1 4 123 34 12 4 123

For the above six arrangements, 1234 is replaced by 1234, such as 1243, 1324, 1342, etc. A total of 24 groups were recorded.

Then the total arrangement method is 24× 6 = 144.