Yes, if you can come up with any of the following:

 * [deterministic finite automaton](https://en.wikipedia.org/wiki/Deterministic_finite_automaton) (DFA),
 * [nondeterministic finite automaton](https://en.wikipedia.org/wiki/Finite_automaton) (NFA),
 * [regular expression](https://en.wikipedia.org/wiki/Regular_expression#Formal_language_theory) (regexp of formal languages) or
 * [regular grammar](https://en.wikipedia.org/wiki/Regular_grammar)

for some language $L$, then $L$ is regular. There are [more equivalent models](https://en.wikipedia.org/wiki/Regular_language#Equivalent_formalisms), but the above are the most common.

There are also useful properties outside of the "computational" world. $L$ is also regular if 

 * it is finite,
 * you can construct it by performing certain operations on regular languages, and those operations are [closed for regular languages](https://en.wikipedia.org/wiki/Regular_language#Closure_properties), such as

      * intersection,
      * complement,
      * homomorphism,
      * reversal,
      * left- or right-quotient,
      * regular transduction

  and [more](https://cs.stackexchange.com/questions/tagged/regular-languages+closure-properties), or
 * using [Myhill–Nerode theorem](https://en.wikipedia.org/wiki/Myhill%E2%80%93Nerode_theorem) if the number of equivalence classes for $L$ is finite.

In the given example, we have some (regular) langage $L$ as basis and want to say something about a language $L'$ derived from it. Following the first approach -- construct a suitable model for $L'$ -- we can assume whichever equivalent model for $L$ we so desire; it will remain abstract, of course, since $L$ is unknown. In the second approach, we can use $L$ directly and apply closure properties to it in order to arrive at a description for $L'$.