Idesperately need can someone explain to me how to do these kinds of questions so i'll be able to get my score higher? ?

Adjacent angles are two angles that have a common vertex and a common side.

<OPN and <TSP have a common side but do not have a common vertex.
<OPN and <RSU do not have a common side or a common vertex.
<OPN and <QPN are adjacent angles. They have a common side and a common vertex.
<OPN and <QPS have common vertex but do not have a common side.

Adjacent angles share a side and have the same vertex point.

When you are given the 3-letter names of the angles, as here, adjacent angles will have 2 letters the same (the common side), and the same middle letter (the common vertex).

The adacent angles in your list are
∠OPN and ∠QPN