Learn Russian: По-нашему, это по-настоящему важная традиция. - In our opinion, this is a truly important tradition.

Yes. Just like по-моему is formed from мой, по-нашему is formed from наш (our). It means "in our opinion" or "in our way." The prefix по- combines with the dative case ending of the pronoun (-ему) to create this adverb of opinion.

Is по-настоящему also one of these special по- adverbs?

Exactly! It translates to "truly" or "genuinely." It is built from the adjective настоящий (real or genuine). By adding the prefix по- and the dative ending -ему, it transforms into an adverb of manner that describes exactly how important the tradition is.

Why do both по-нашему and по-настоящему have hyphens?

Russian has a strict spelling rule for this exact grammar point: when an adverb is formed with the prefix по- and ends in -ому, -ему, -ски (like по-русски), or -ьи, it must always be written with a hyphen.

Is the comma after По-нашему mandatory?

Yes. Whenever you use introductory words that express an opinion or a subjective viewpoint, such as по-моему, по-нашему, or по-вашему, you must separate them from the rest of the sentence with a comma.