Commentaries:
It is important to note that there is no command from God to observe the new moon in either Testament. Instead, they are presented as a recognized and ongoing practice to which God adds special sacrifices and offerings. These additions elevate them above an ordinary day but not to the level of a holy day.
John W. Ritenbaugh
The New Moons
Notice that the word "its" appears twice, conveying that the meal offering belonged to the burnt offering. This demonstrates that the two offerings were offered together. Though the burnt offering may appear to be the "greater" of the two, one is incomplete without the other, even as the two great commandments go together. In each case, the one shows man doing his duty to God, the other, his duty to man.
I John 4:20-21 confirms this:
If someone says, "I love God," and hates his brother, he is a liar; for he who does not love his brother whom he has seen, how can he love God whom he has not seen? And this commandment we have from Him: that he who loves God must love his brother also.
The two must go together. The one without the other is not acceptable to God.
John W. Ritenbaugh
The Offerings of Leviticus (Part Three): The Meal Offering
Other Forerunner Commentary entries containing Numbers 29:6:
2 Chronicles 2:4