How to decompose a permutation into a product of transpositions?

Question

Mathematics

Please explain in an accessible language how to decompose substitutions into a product of transpositions?
As far as I understand, if there is a substitution:
1 2 3 4
2 1 4 3
Then its transposition is
1 2 3 4
1 2 4 3
That is, we simply make one transposition in the lower permutation. This transposition can be written as (2 1).
But I don’t understand how to decompose a permutation into a product of transpositions (((
In Kurosh’s textbook there is an example of decomposing a permutation into a product of transpositions. I noticed such a thing that the product of transpositions in its pure form cannot serve as an algorithm for reducing a permutation to an identical one:

Why So?