What does this example mean? Slow cooling of 40% Sn alloy from 800°C to 600°C: L → L and γ → L, γ, and ε → L and ε
Consider the 40 at% (Sn) composition at 800 °C: it's a liquid.
When you cool it down at around 650 °C you enter a two-phase field: the solid gamma forms (Cu-enriched) and the liquid enriches in Sn. As you further cool down the gamma phase will continue to form, but with progressively higher content of Sn
You cool down at 640 °C and you enter a new different two-phase field: the liquid partially reacts with the gamma phase forming the solid epsilon phase. If you further cool down, the ε phase will continue to form from the liquid, but its composition will progressively enrich in Cu.
Just below 415 °C you enter into another two-phase field: the liquid will solidify into ε and η phase.
That's what occurs by cooling down to 300 °C, but if you further would cool down below 189 °C you will enter another two-phase field; in this case the ε and η' phases will form.
The amounts of the different phases at the different $T$ are obtained by applying the lever rule.
Take care, I described what happened from the thermodynamic point of view (that is what is represented in a phase diagram); the kinetics can remarkably change the things.