“From the mouths of babes and infants you have established strength.” The Septuagint version of this verse is quoted in Matthew 21:16. It seems that the early translators quoted the Septuagint in Matthew because the meaning of the Hebrew text is unclear.
“to silence the enemy.” The Hebrew is more literally, “to cause to cease” an enemy. This can be to “silence” them, or perhaps it even has eschatological implications pertaining to Judgment Day, and “put an end to” (NET) is also part of the meaning. Although the meaning is not explained, it likely has to do with innocent and honest people praising and supporting God against His enemies, who have a demonic agenda.