Your parent is asking how the planet orbits two stars, and probably how the 2-star-1-planet system orbits the two other stars. That is, "how does any body orbit two stars?"
Normally, it doesn't orbit two stars, it orbits their combined center of gravity (which, if the stars were the same mass, would lie exactly between them). Or to be more precise, both the stars and the planet together orbit their combined center of mass.
And I explained. How does the Earth orbit the Sun-Mercury system? It's no different than how a planet orbits a binary system from afar. The two stars orbit each other and then the planet orbits around both stars. And then that whole system orbits around another binary star system at a tremendous distance (1,000 AU, ten times farther away than Voyager 2 is from the Earth now).
It's a little different; in our solar system, the Sun is one of the foci of the ellipse, whereas in a binary system that focus would instead be the center of gravity between the two stars.
Yes, though in this case the big star weighs nearly 4x as much as the little star, so it's a matter of one star shuffling around in a small ellipse with the smaller star in orbit, rather than a more intimate orbital dance if the stars had been closer in mass.
We still have an analogy in the Solar system, Hydra and Nix orbit the Pluto-Charon binary.
The barycenter of the Pluto system is outside the surface of the dwarf planet.
Although Mercury in this instance is extremely insignificant, technically the earth orbits the center of gravity of the Sun and Mercury. Actually, the center of gravity of the Solar system as a whole, but I'm just going along with the GP.
Its complicated. You can approximate it using the 2-star-center-of-mass, but thats skipping over important stuff.
See, the stars are orbiting one another. At any time one may be closer/further away than the other from the planet. That makes the COG appear to 'wobble'.
IF the planet is in something like a 'lagrange point' where it always sees both stars in the same relative position, then the COG approximation is true. Otherwise the planet will behave in a more complicated manner, and in fact may not have a stable orbit at all.
