Q: How does the Gemara know that yom hashishi means the sixth of Sivan? Isn’t it talking about the sixth day of creation?
A: The Gemara (Avoda Zarah 3a) says that the Torah is hinting to us that all of creation is dependent on the Am Yisroel accepting the Torah. That’s how the Chachomim explain the possuk, "And it was evening and it was morning; it was the sixth day." They took note of the fact that it doesn’t say yom shishi the way it says by all the other days, yom sheini, yom shlishi, yom revi’i. It says yom ha’shishi, the sixth day; a special sixth day. And the Gemara says there that it’s talking about Shavuos, the sixth of Sivan.
So we read the possuk like this: The creation of day and night, that means the creation of the world, you know when it was? It was on yom hashishi, on that sixth day of Sivan when the Am Yisroel accepted the Torah; that’s when the world was created. Because Matan Torah is the fulfillment of the creation of the world. If not for Matan Torah, the whole creation would have been a waste.
Now how does the Gemara know that? And the answer is it's written in big characters all over the entire Chumash. As follows: Let's say that you enter a house and you see on the walls a picture of the master of the house; a big picture. Then you see his diploma hanging on another wall. Then you see on another wall a framed testimonial that his local synagogue presented to him.
So you start thinking, “Probably this man is somebody important in this house.” At least he thinks he's important. Because on all sides there are mementos to remind you of him. His personality is being displayed on all sides. Here is his big Morris chair where he sits in the evening. Here is his box of favorite cigars. The man is all over the place even though you don't see him right now. Here are his slippers. Here is his favorite place where he sits by the television, where he munches let's say. He munches peanuts or whatever it is. The man is all over the place. All you need is he should come in and show himself.
Now, when you look lehavdil at the Torah, what do you see in the Torah? You see one thing in the Torah, and that's Torah. Wherever you look in the Torah, you see Torah. You see learning Torah. You see keeping the Torah. It's reiterated again and again. If there's anything conspicuous in the Chumash it's Torah.
Now, if the creation of the world was paramount in the Mind of Hakadosh Baruch Hu then that's all we should talk about. Torah? Alright. You put it someplace in the corner. You mention it in passing. But the continents! That should be the main subject! Why shouldn't there be a sefer, not Bereishis, not Shemos, not Vayikra, but a sefer Europe and Asia, a sefer North and South America, a sefer Africa? Let's study geography. Or the Chumash should talk about astronomy; this galaxy, this solar system. There's so much to talk about in the world and they're all wonders. It should talk about the nature of insects; the wonderful instincts you see in animals. There's so much to speak about in flowers. There's no end to the beauties and wonders of nature that demonstrate the Hand of Hakadosh Baruch Hu on all sides. It would bring you to a lot of emunah.
But all that valuable space is sacrificed and it's all for Torah. Again and again, it says “Keep My laws,” “Study My laws.”
What do we see here? We see that that's what the Torah is talking about; not the creation of the world. And therefore it stands to reason whether you'll interpret vayehi erev vayehi boker yom hashishi means the sixth day of creation or something else makes no difference. It's as clear as if it had been there. Just like the man in the house, his pictures are all over the place, his things are all over the place and so we see that the man is demonstrating his personality.
And because the Torah demonstrates that everything depends on Torah so we understand that all of creation is dependent, is hanging, on the sixth of Sivan when the Am Yisroel accepted the Torah.