For the question: "My quadrilateral has a pair of equal sides and a pair of parallel sides, what special type my quadrilateral must be, and would it could be," the answer was that it must be a trapezoid, and could be an isosceles trapezoid, parallelogram, rhombus, rectangle, square, and right trapezoid. Why is this?

Step-by-step explanation:

It must be a trapezoid because a trapezoid has at least one set of parallel sides.  Sides of equal length don't mean anything really unless we know hose sides are parallel.  I will say sometimes I hear trapezoids ONLY have two parallel sides, while the other two are not, while in other places as long as two are parallel it is a trapezoid.  It looks like for this question it is using the definition that at least two parallel sides makes it a trapezoid.

it can be an isosceles trapezoid since it is a type of trapezoid,  same with right trapezoid.  Basically any special kind of trapezoid

parallelogram because it can have two pairs of parallel lines and have thos parallel sides be equal.  So this also means it can be all kinds of parallelograms.  

Do you have a list to choose from?  because most I pull up don't include right trapezoid at least.

This leaves kite as the only kind of quadrilateral to look at yet, and it specifies no parallel sides. bt your shape need at least one set of them, so it cannot be a kite.