Statistics: sampling distributions related to normal distribution

http://www.geocities.com/asdfasdf23135/stat1.JPG

iid=independent and identically distributed

This is the model answer to a question which is unlikely to be wrong. I don't understand the part circled in red. How is that step *justified*? ~ is not the same as a equal sign, so can we still do that?

In other words, my question is "If c is a constant and cW follows the t-distribution with parameter 12, i.e. cW~t(12), does this imply that W~1/c t(12)?"

If so, WHY?

I hope that someone can help me out. Thanks a lot!