This parsha brought a very exciting moment to the Jewish world. In the middle of Parshat Shemini in pasuk 10:16, we find the expression, "Moshe inquired insistently about the he-goat of the sin-offering..." In Hebrew the wording is "V'et s'ir ha'chatat darosh darash..." The words darosh and darash are spelled the same. They are also the exact center of the Torah, the half-way point.
We have now officially completed more than half of the Torah.
On the side of the first half is the word darosh, which means to ask or investigate. In other words, to delve and learn Torah. On the other side is the second word darash, which means to give over (a sermon) or to teach.
Just as the center of the Torah is darosh and then darash - learning the Torah and then teaching it - so the center of our lives as well must be learning and studying and understanding the Torah, and then giving it over to others.