Albert Barnes on Matthew 16:20

Then charged, etc. That is, he then commanded them. Mark Mk 8:30 and Luke Lk 9:21 (Greek) that he strictly or severely charged them. He laid emphasis on it, as a matter of much importance. The reason of this seems to be that his time had not fully come; he was not willing to rouse the Jewish malice, and to endanger his life, by having it proclaimed that he was the Messiah. The word Jesus is wanting in many manuscripts, and should probably be omitted. "Then he charged them strictly to tell no man that he was the Christ or Messiah."

(v) "Then charged" Mk 8:30