we know that
When two chords intersect each other inside a circle, the products of their segments are equal (Intersecting Chord Theorem)
so
in this problem
AE*EB=DE*EF----> EB=DE*EF/AE
AE=4 in
DE=12 in
EF=8 in
EB=?
EB=DE*EF/AE-----> EB=12*8/4----> EB=24 in
the answer is
EB=24 in