Comments for 右

The stroke order above is correct. I don't know which book you use, but it is also the same in Genki.

Yep, the stroke order here is correct.

One way to remember which stroke is first for 右 compared to 左 is that strokes for both of these always alternate between horizontal and vertical.

So 左 is horizontal-vertical-horizontal-vertical-horizontal

and 右 is vertical-horizontal-vertical-horizontal+vertical-horizontal

Correct me if I'm wrong, but for migi I believe it is horizontal-vertical-vertical-horizontal&verticle-horizontal

I double checked it in genki, I appologize, I was wrong

Why does stroke order matter, though?

This is an interesting one. The correct order in Chinese starts with horizontal - vertical, just like hidari. And I'm pretty sure I remember the official order being changed in Japan ten or more years ago (correct me if I'm getting confused with some other kanji). 

When inconsistencies like this don't have any obvious historical or other justification, I stick with what I learned for Chinese or what I learned when beginning Japanese. 

The stroke order is just to make the drawing/writing easier, you don't necessarily have to follow it, though at the very least you should start from top to bottom and left to right. Starting bottom right with the strokes would be weird and the kanji would most definitely look bad too.