How does SQL's LIKE work in case of Path Enumeration?

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I am reading the book SQL Antipatterns where a SQL query is used like this:

SELECT *
FROM Comments AS c
WHERE '1/4/6/7/' LIKE c.path || '%';

to find ancestors of comment #7 from this table:

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I am not much familiar with the regex employed for LIKE and would appreciate understanding how it does its work. Specifically, does it matter that the literal '1/4/6/7' is located on the left hand of the LIKE keyword? And how does the entire WHERE predicate work (i.e. || '%')?

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