Explanation:
you know the meaning of the words "parallel" and "skew" ?
and the difference between a line and a plane (not the one that flies through the air ...) ?
let's start with "line" :
a line is a completely straight "string" that is defined by at least 2 points. these points are either beginning and end of that "string", or the "string" goes through them and extends beyond them without deterring from the direction and inclination between the 2 points.
then a "plane" :
this is like a giant sheet of paper that is completely flat and defined by at least 3 points. it either ends with the defining points or goes on indefinitely beyond the points by keeping its orientation and "flatness" from the area between the points.
parallel lines :
these 2 "strings" run along to each other (if necessary in all eternity) without ever getting closer to or farther away from each other. no matter from what angle you look at them, they will never not even seemingly cross each other. but from a certain angle you would only see one string, because one is completely covering the other.
parallel planes :
similar to parallel lines - these 2 sheets of paper will never get closer to or farther away from each other for any point on them. they are like the old "double-winged" airplanes, where there were a pair of wings on either side of the airplane. and each wing in such a pair of wings would be competent parallel to the other.
In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel (this is not possible in 2- dimensional space, because there, if 2 lines are not parallel, then they must intersect each other at one point somewhere).
so, now to the answers :
parallel to XT are clearly SW, VZ, UY
parallel to ZY are clearly WX, VU, ST
parallel to VS is only ZW
parallel to STU is WXY
parallel to UVZ is TSW
skew to SW are VU, UT, ZY, XY (while XT, VZ, UY are parallel and therefore not skew)
skew to UT are ZW, SW, VZ, WX, ZY (all others are either parallel or cross UT - special case VS, which will cross UT outside of the drawn object, but it will cross the line further out in the back)