[NOTE: Steps within this Main Quest can be completed before others. However, it is recommended that you do the first two before this one, otherwise the Black Egg might lodge itself out of the Pyramid, locking you out of quest completion.]
After the excavation of Tunnel 6, a mysterious sphere ("Black Egg") will have appeared near the M16 wallbuy.
The sphere must be knifed/shot in order to begin moving it. It will bounce around Tunnel 6 multiple times, sometimes getting stuck on a wall or ceiling, required to be knifed/shot again to continue moving. Eventually, it will reach an area above two barrels, close to the MPL wallbuy - after which, it will patiently wait for you at the door to leave Tunnel 6.
Once outside, the egg will float up to a satellite dish above the Receiving Bay.
In order to dislodge the egg, it must be shot with a blast from the Wave Gun - after which, it will float down to Tunnel 11.
Within Tunnel 11, it will once again bounce around a few different places, before lodging itself in a somewhat hard-to-spot corner nearby the Semtex wallbuy. Indeed, a Semtex or weapon that deals explosive damage (including the Ray Gun) will dislodge it from this corner. It will then bounce several more times, before heading towards the door leading to the Pyramid, where it will insert itself into the Mythos Disc.
Proceed to Step 5.