Follow the map

Two things to notice:

(a) A fold can only occur when a given line is made of segments which are of the same nature (all valleys or all creases).

(b) Upon folding the valleys should be folded on a crease and vice-versa.

From there it is easy to check that Pattern B may not be folded. The only fold with which one could start with is the rightmost vertical line (it's the only line where each segment is of the same nature). But then remaining picture has no possible folds (all lines have segments of distinct nature).

The answer is $\fbox{Pattern B}$ .

How to fold the rest?

Pattern C is the easiest to fold: (1) fold along the horizontal line [a valley] (2) fold the remaining vertical lines in any order

Pattern D: (1) fold along the middle vertical line [a crease] (2) fold along the (only) remaining vertical line (3) fold one last time

Pattern A: (1) fold along the rightmost vertical line [a valley] (2) fold along the two remaining vertical lines (in any order) (3) fold along the remaining horizontal line.

Each $+$ shape of folds is folded along two lines:

• The first line to be folded will be the same type of fold along its length (as it has not been broken by another fold).
• The second line will be half a valley fold, and half a mountain fold, because of the initial fold.

This results in a T shape of one fold type, with the remaining fold being the other type.

The $+$ creases in A, C & D all consist of this pattern, whereas in $\boxed{\mbox{Pattern B}}$ , there are creases which do not follow this pattern.

Lets look at the three crease intersections inside the map rectangle: Each of these has four creases coming out of it. The four creases are results of two folds along two perpendicular directions (horizontal and vertical). The fold that occurred first left two creases of the same type (i.e. both valley or mountain) along one direction. The second fold then left two creases of different types along the other direction (i.e. one valley and one mountain). That means there have to be exactly three creases of the same type coming out of each of these points. The only pattern that violates this rule is B which has two points with two valleys and two mountains.

(You could, if you like, assign values $-1$ and $+1$ to valleys and mountains respectively. When you sum up the values of creases coming from any intersection point you should always get $\pm1$ )

It wasn't really necessary to trace the whole step to know if the folding pattern will work. Since we are only concerned of what doesn't work, all we need to know is that when folding the roadmap either just horizontally or vertically (no complicated setup as such on origami) we can say that there should be at least one whole straight valley or straight whole mountain that goes completely horizontally or verticllay (this is where you would probably fold it first). And if it does, there may be one if it was located at the middle (Pattern C), otherwise it should be symmetric, there should be a pair at both halves in reference to the middle fold. See image below.

As what we can see, Only B failed to satisfy this characteristic therefore the answer is Pattern B .

I went by trial and error, since I have exceptional visual ability I mentally tested them in my head, figured it was B, then took a piece of paper and confirmed my hypothesis by simply showcassing that it is impossible to do the valley crease after a cornered double mountain crease.