I was practicing for my SAT with the official SAT questions when I came across this one and was quite confused.
[![enter image description here](https://i.stack.imgur.com/mYR64.jpg)](https://i.stack.imgur.com/mYR64.jpg)

Why is the semicolon placed AFTER "however" (see picture)?

I get the need for a semicolon to be used but I am quite confused about the position of where the semicolon is placed. I always thought that the semicolon should be placed before the adverb connecting the two independent clauses. E.g.- He went to bed early; however, he didn’t get much sleep.

I also don't understand the part of the explanation where the position of semicolon indicates that the information is contrary to the previous sentence.

Is there a rule of thumb I can use to determine where the semicolon should go?

Thanks!!