Answer:
"While"
Step-by-step explanation:
A subordinating conjunction is a conjunction that is used to introduce the dependent clauses in a sentence. And some subordinating conjunctions also have other functions according to their use.
In the given sentences "I rode my bike" and "My brother mowed the front yard", these two sentences can be joined by using the time subordinating conjunction such as "while, after, before, as soon as, since, when, as" etc.
Thus, the final sentence will be (using while)
While I rode my bike, my brother mowed the front yard.