How can I show this language is Regular? (Foundations of computing)
Your question was already asked before, but got no answer: How to prove for string of triplets that it is a Regular Language?. I merely summarize the comments given there.

You need to implement binary addition. That is easier when you consider first the language in reverse, the lower bits first.

Standard letters are (in a more intuitive notation) [00|0], [01|1], [10|1], [11|0]. In the last case however, we realize that we should take a carry to the next position. This can be solved by adding a special state for that case, and adapting the letters accordingly.