To solve this problem, we need to use the Angle Bisector Theorem. According to this theorem, if a line divides the opposite side of a triangle in the ratio of the other two sides, then it is an angle bisector of the opposite angle.

In the given triangle, we have:

\(\frac{AB}{AC} = \frac{BD}{DC}\)

This means that \(AD\) is the angle bisector of \(\angle BAC\). Therefore, \(\angle BAD = \angle DAC\).

Given \(\angle BAD = 28^\circ\) and \(\angle DAC = 28^\circ\), the total angle at \(A\) is:

\(\angle BAC = \angle BAD + \angle DAC = 28^\circ + 28^\circ = 56^\circ\)

We also know that \(\angle ACD = 60^\circ\).

Since \(\angle ACD\) and \(\angle ABC\) are angles of triangle \(ABC\), we can use the triangle angle sum property:

\(\angle ABC + \angle BAC + \angle ACD = 180^\circ\)

Substituting the known values, we get:

\(\angle ABC + 56^\circ + 60^\circ = 180^\circ\)

Solving for \(\angle ABC\):

\(\angle ABC = 180^\circ - 56^\circ - 60^\circ = 64^\circ\)

Therefore, the correct answer is

$64^\circ$

.