Now comes easy Gemara…
Mishna: Beis Shammai: A ladder cannot be moved from one dovecote to another But it can be moved from one window to another. Beis Hillel permits this.
We see from here that regarding simchas Yom Tov, Beis Hillel is lenient and Beis Shammai is stringent.
Challenge: Mishna (001): “Beis Shammai: He may dig with a stick and cover the blood. Beis Hillel: He may not slaughter unless he has earth prepared for the purpose of covering.” [So we see that Beis Hillel are stringent even when it comes to matters of simchas Yom Tov, and they should be constant in their principles applying them across the board].
Rabbi Yochanan: The subject is inverted, Beis Hillel is the stringent one with regard to moving the ladder.
Challenge: Perhaps their positions are unique to the circumstances in each case. Beis Shammai is only lenient in the first case because a stick has already been placed in the ground before Yom Tov. Beis Hillel is lenient in the second case because the dovecote demonstrates why he’s carrying the ladder.
Resolution: This is the reason Rabbi Yochanan felt it necessary to invert our Mishna:Mishna (040): Beis Shammai: [Animals may not be handled on Yom Tov, they’re muktzeh] One may not take a bird on Yom Tov [to slaughter for the meal] unless he had hefted it from before Yom Tov [out of concern that when he picks it up he’ll find it too lean and will want to choose another one for his meal, he will then be guilty of having picked up a muktzeh bird without the excuse of needing it for simchas Yom Tov]. Beis Hillel: He can designate them before Yom Tov.So we see that Beis Hillel is lenient because of simchas Yom Tov in opposition to our Mishnah (036)?
Rabbi Yochanan: The subject is inverted, Beis Hillel is the stringent one with regard to picking up the bird.
Challenge: Perhaps their positions are unique to the circumstances in each case. Beis Shammai is only lenient in the first case because a stick has already been placed in the ground before Yom Tov. Beis Hillel is lenient in the second case because muktzeh can be permitted by designation.
[Rashi teaches that in all these cases (we will learn more tomorrow), the second Mishna is inverted while the original Mishna remains. Tosfos argues that it isn’t logical to invert multiple Mishnayos because of one Mishna, and it is the first Mishna which should be inverted according to Rabbi Yochanan.] 
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