We generally surround a subordinate clause with paired punctuation when it is "unnecessary" (sometimes called "removable", "parenthetical", etc.). That would apply to your first sentence:

He doesn’t like flying, though he enjoyed his trip to Italy last year.¹

If we consider the clause important to the sentence's meaning, then we omit paired punctuation:

You got that problem wrong because you wrote "12" though the correct answer is actually "11".

The same principle applies to your second sentence. Furthermore, another rule says that a modifier² at the beginning of a clause may generally be followed by a comma. Thus:

Though he enjoyed his trip to Italy, he does not like flying.

In your last sentence, the subordinate clause seems unnecessary, so I would include the punctuation:

Moving abroad is not helpful in terms of family development, though it may be good for education and job prospects.³

¹The second comma of the pair is "absorbed" into the period at the end of the sentence.
²I'm using this word, but terminology will vary.
³I deleted the first part of this sentence, which is irrelevant for this issue, and deleted "the" for idiomaticness.

We generally surround a subordinate clause with paired punctuation when it is "unnecessary" (sometimes called "removable", "parenthetical", etc.). That would apply to your first sentence:

He doesn’t like flying, though he enjoyed his trip to Italy last year.¹

If we considered the clause important to the sentence's meaning, then we would omit paired punctuation:

You got that problem wrong because you wrote "12" though the correct answer is actually "11".

The same principle applies to your second sentence. Furthermore, another rule says that a modifier² at the beginning of a clause may generally be followed by a comma. Thus:

Though he enjoyed his trip to Italy, he does not like flying.

In your last sentence, the subordinate clause seems unnecessary, so I would include the punctuation:

Moving abroad is not helpful in terms of family development, though it may be good for education and job prospects.³

¹The second comma of the pair is "absorbed" into the period at the end of the sentence.
²I'm using this word, but terminology will vary.
³I deleted the first part of this sentence, which is irrelevant for this issue, and deleted "the" for idiomaticness.

We generally surround a subordinate clause with paired punctuation when it is "unnecessary" (sometimes called "removable", "parenthetical", etc.). That would apply to your first sentence:

He doesn’t like flying, though he enjoyed his trip to Italy last year.¹

If we consider the clause important to the sentence's meaning, then we omit paired punctuation:

You got that problem wrong because you wrote "12" though the correct answer is actually "11".

The same principle applies to your second sentence. Furthermore, another rule says that a modifier at the beginning of a clause may generally be followed by a comma. Thus:

Though he enjoyed his trip to Italy, he does not like flying.

In your last sentence, the subordinate clause seems unnecessary, so I would include the punctuation:

Moving abroad is not helpful in terms of family development, though it may be good for education and job prospects.²

¹The second comma of the pair is "absorbed" into the period at the end of the sentence.
²I deleted the first part of this sentence, which is irrelevant for this issue, and deleted "the" for idiomaticness.

We generally surround a subordinate clause with paired punctuation when it is "unnecessary" (sometimes called "removable", "parenthetical", etc.). That would apply to your first sentence:

He doesn’t like flying, though he enjoyed his trip to Italy last year.¹

If we consider the clause important to the sentence's meaning, then we omit paired punctuation:

You got that problem wrong because you wrote "12" though the correct answer is actually "11".

The same principle applies to your second sentence. Furthermore, another rule says that a modifier² at the beginning of a clause may generally be followed by a comma. Thus:

Though he enjoyed his trip to Italy, he does not like flying.

In your last sentence, the subordinate clause seems unnecessary, so I would include the punctuation:

Moving abroad is not helpful in terms of family development, though it may be good for education and job prospects.³

¹The second comma of the pair is "absorbed" into the period at the end of the sentence.
²I'm using this word, but terminology will vary.
³I deleted the first part of this sentence, which is irrelevant for this issue, and deleted "the" for idiomaticness.