Here is the original item:
Mackenzie had to leave the room,
(A) for her
father was noisily crunching raw radishes,
(B) which
produced so annoying a sound
(C) that
studying was impossible.
You wanted to do this:
McKenzie had to leave the room, for her father
was noisily crunching raw radishes, which
produced so annoying a sound;
that studying was impossible.
Adding a semicolon after sound makes a fragment. That studying was impossible is a subordinate clause. You cannot connect a subordinate clause with such a strong mark of punctuation.
You might want to review the rules.