The toilet paper cover is stranded knitting and yes, you can do it holding one color in each hand (very convenient, I do it this way too), but you don't have to. This site has a video about stranded knitting. Amy has a way she holds both colors in her left hand (for Continental knitting), I think it looks wonderful, but I can't do it.
You can do it any way you can to knit with first one color and then the other. You can do both colors with one hand dropping the one color and picking up the second one and working back and forth that way. It is a little slower, but perfectly acceptable.
To find the video, hold your cursor on "View videos" and then choose "Advanced Techniques" Scroll down to something like "Working with 2 colors at the same time" and then look at "Stranded Knitting".
It is not hard to do, you just have to be careful and be sure to tug to keep the floats loose. That is a biggie.