How do you know when to use the distributive property when solving equations?
It is one part of the "toolbox" of functions. Use it when possible to simplify an expression for solving.
All mathematical functions and properties are just tools for manipulating expressions in a logical manner to derive a useful result.
None are "required" to be used at any time - it is just the convenience of the user. There are often more than one way to solve a particular problem. The sequence may seem more understandable in one form to one person than another. There are recommended and common practices that have developed because of their consistent utility. That is why courses involve a lot of examples for students.
For example, the expression
In general, you may use the distributive function whenever there are elements of an expression that are distributed. Some good examples are here: