A wire with a resistance of 15.0 is formed into a regular hexagon...

Total resistance of the wire is $15.0 \Omega$.

Since the wire is formed into a regular hexagon, it is divided into $6$ equal sides. The resistance of each side is $\dfrac{15.0}{6} = 2.5 \Omega$.

Points $A$ and $D$ are opposite vertices of the hexagon. The circuit between $A$ and $D$ consists of two parallel paths: path $ABCD$ and path $AFED$.

Each path contains $3$ sides in series. The resistance of each path is $3 \times 2.5 = 7.5 \Omega$.

The equivalent resistance $R_{eq}$ between $A$ and $D$ is the parallel combination of these two paths:

$R_{eq} = \dfrac{7.5 \times 7.5}{7.5 + 7.5} = \dfrac{7.5}{2} = 3.75 \Omega$