To answer this question, we need to look at where to use semicolons and commas.
Semicolons can only be used when linking two independent clauses. A good way to see if you could use a semicolon is to read the two parts by themselves, and see if they work as sentences.
On the other hand, commas are used to link two clauses which have a connecting word, such as and, for, but, etc. For example, a comma would be used in the sentence "I ran to the store, and I got lost". This is because the word and was used after the comma. One way to remember these connecting words (coordinating conjunctions I believe is the proper name) is the acronym FANBOYS, which stands for for, and, nor, but, or, yet, and so.
Now, when we look at this question, let's look at where the problem area is. The sentence without any punctuation is: My father is flying in from overseas tomorrow ___ the arrival time is 4:45 PM.
We can first rule out C as you cannot just put two clauses together without any punctuation between them.
Going back to what we looked at, let's look at the one comma case, or B. In the case of this, there is no coordinating conjunction linking them, so this is incorrect.
Now the two semicolon cases. When you look at them on their own, you see that separating D into two independent clauses does not work, as "and the arrival time is 4:45 PM" is not a sentence. On the other hand, separating A into two independent clauses does work, as the two parts can be read as independent sentences.
Therefore, your answer is A.
