Sentence examples for both of those things from inspiring English sources

"both of those things" is a grammatically correct and commonly used phrase in written English.
It is typically used to refer to two specific items or ideas that have been previously mentioned or are known to the speaker and the listener. Example: "I'm considering buying a new car, but both of those things are important to me: good fuel efficiency and a spacious interior." In this example, the speaker is discussing two specific qualities they are looking for in a new car, and they are emphasizing that both of these things are equally important to them.