Step 1: Picture what happens on cooling.
Imagine taking a steel with, say, 0.4% carbon (well below the eutectoid value of 0.8% C) and slow cooling it down from the austenite field. As soon as the temperature drops below the $A_3$ line, the austenite can no longer hold onto all its iron atoms in the FCC form, so pure iron atoms start rejecting themselves out as BCC ferrite while the remaining austenite gets richer in carbon.
Step 2: Why this ferrite is called "proeutectoid".
This ferrite appears before the alloy ever reaches the eutectoid temperature of $723^\circ C$, so it earns the name proeutectoid ferrite ("pro" meaning before). It keeps forming at the grain boundaries until the leftover austenite has been enriched to exactly the eutectoid composition, at which point that remaining austenite converts to pearlite.
Step 3: Checking the other steel types.
A eutectoid steel starts out already at 0.8% C, so it has nothing to reject before pearlite forms, there is no proeutectoid stage at all. A hyper eutectoid steel (above 0.8% C) rejects the opposite phase, proeutectoid cementite, not ferrite. White cast irons sit at even higher carbon and solidify with massive cementite, again no proeutectoid ferrite.
Step 4: Matching to the option.
Only steels with carbon below the eutectoid point, that is, hypo eutectoid steels, show this proeutectoid ferrite in their final structure.
\[ \boxed{\text{Hypo eutectoid steels}} \]