Option A is correct.
"We have to master the routine during this morning's practice; otherwise, the coach says we will have to work a second (II) day."
"otherwise, the coach says we will have to work a second (II) day" is telling why they have to master the routine; therefore a semicolon is used.
A, because the semi-colon is separating the other thought.
Option A is the only correctly punctuated sentence, using a semicolon before the transitional word 'otherwise' to separate two independent clauses. The other options either misuse colons or commas. When using transitional words between independent clauses, a semicolon is appropriate.
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