The speed of light is constant for all observers, so if Stanley sees it reach A’ and B’ simultaneously, then Mavis must see it reach B’ first, as you said. The diagram shows that this occurs, from Stanley’s perspective, because Mavis is moving to the right and the light from B’ reaches her before the light at A’. Of course, she thinks that the velocity of light from both sources relative to her is identical, so she must conclude that lightning struck B’ earlier since the light from this event reached her first. This thought experiment shows that Mavis must observe a time difference, so if Stanley records the strikes using synchronized clocks, Mavis will see them as non-synchronized. This is the only way to preserve her view of events. The thought experiment of Stanley using synchronized clocks actually demonstrates that, in relativity, spatially separated clocks which are synchronized in one frame of reference may not be synchronized in another. This can be seen in the Lorentz transformation for time: If two observers moving relative to one another, A and B, start at the same position with initially synchronized clocks, and observer A then records time $t$ at position $x$, observer B moving relative at velocity $v$ in the $x$-direction will record time $t'=\gamma\big(t-\frac{vx}{c^2}\big)$, where $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$. The change in recorded time in this formula depends on position, which demonstrates how two distant clocks may appear synchronous in one frame of reference but not another.

The speed of light is constant for all observers, so if Stanley sees lightning reach A’ and B’ simultaneously, then Mavis must see it reach B’ first, as you said. The diagram shows that this occurs, from Stanley’s perspective, because Mavis is moving to the right and the light from B’ reaches her before the light at A’. Of course, she thinks that the speed of light from both sources relative to her is identical, so she must conclude that lightning struck B’ earlier since the light from this event reached her first. This thought experiment shows that Mavis must observe a time difference, so if Stanley records the strikes using synchronized clocks, Mavis will see them as non-synchronized. This is the only way to preserve her view of events. The thought experiment of Stanley using synchronized clocks actually demonstrates that, in relativity, spatially separated clocks which are synchronized in one frame of reference may not be synchronized in another. This can be seen in the Lorentz transformation for time: If two observers moving relative to one another, A and B, start at the same position with initially synchronized clocks, and observer A later records time $t$ at position $x$, observer B moving relative at velocity $v$ in the $x$-direction will record time $t'=\gamma\big(t-\frac{vx}{c^2}\big)$, where $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$. The change in recorded time in this formula depends on position, which demonstrates how two distant clocks may appear synchronous in one frame of reference but not another.

The speed of light is constant for all observers, so if Stanley sees it reach A’ and B’ simultaneously, then Mavis must see it reach B’ first, as you said. The diagram shows that this occurs, from Stanley’s perspective, because Mavis is moving to the right and the light from B’ reaches her before the light at A’. Of course, she thinks that the velocity of light from both sources relative to her is identical, so she must conclude that lightning struck B’ earlier since the light from this event reached her first and both points are an equal distance from her. This thought experiment shows that Mavis must observe a time difference, so if Stanley records the strikes using synchronized clocks, Mavis has to see them as non-synchronized. This is the only way to preserve her view of events. The thought experiment of Stanley using synchronized clocks actually demonstrates that, in Relativity, spatially separates clocks which are synchronized in one frame of reference may not be synchronized in another.

The speed of light is constant for all observers, so if Stanley sees it reach A’ and B’ simultaneously, then Mavis must see it reach B’ first, as you said. The diagram shows that this occurs, from Stanley’s perspective, because Mavis is moving to the right and the light from B’ reaches her before the light at A’. Of course, she thinks that the velocity of light from both sources relative to her is identical, so she must conclude that lightning struck B’ earlier since the light from this event reached her first. This thought experiment shows that Mavis must observe a time difference, so if Stanley records the strikes using synchronized clocks, Mavis will see them as non-synchronized. This is the only way to preserve her view of events. The thought experiment of Stanley using synchronized clocks actually demonstrates that, in relativity, spatially separated clocks which are synchronized in one frame of reference may not be synchronized in another. This can be seen in the Lorentz transformation for time: If two observers moving relative to one another, A and B, start at the same position with initially synchronized clocks, and observer A then records time $t$ at position $x$, observer B moving relative at velocity $v$ in the $x$-direction will record time $t'=\gamma\big(t-\frac{vx}{c^2}\big)$, where $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$. The change in recorded time in this formula depends on position, which demonstrates how two distant clocks may appear synchronous in one frame of reference but not another.