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Edit:

中国人：你的中文是[在哪里]学的？ indicates the question is asking 'where'

中国人：你的中文是[怎么]学的？ indicates the question is asking 'how'

中国人：你的中文是[从哪里]学的？ indicates the question is asking 'from what source' And sources are not locations -- For example: from books, from classes, from T.V.

'From what source' = 'with what methods' --> 'how' you learn

When the Chinese person asked '在哪里学的' but claim he was asking "how" he should have said 从哪里 instead of 在哪里

'在哪里' refers to 'what location' e.g. Hong Kong, Beijing, Shanghai.

'从哪里' refers to 'source' e.g. books, classes, the internet.

Does 「你的中文是在哪里学的？」mean “How did you study Chinese?” or “Where did you study Chinese?”

It means “Where did you study Chinese?"

Edit:

中国人：你的中文是[在哪里]学的？ indicates the question is asking 'where'

中国人：你的中文是[怎么]学的？ indicates the question is asking 'how'

中国人：你的中文是[从哪里]学的？ indicates the question is asking 'from what source' And sources are not locations -- For example: from books, from classes, from T.V.

'From what source' = 'with what methods' --> 'how' you learn

When the Chinese person asked '在哪里学的' but then claimed he was asking "how" he should have said 从哪里 instead of 在哪里

'在哪里' refers to 'what location' e.g. Hong Kong, Beijing, Shanghai.

'从哪里' refers to 'source' e.g. books, classes, the internet.

Does 「你的中文是在哪里学的？」mean “How did you study Chinese?” or “Where did you study Chinese?”

It means “Where did you study Chinese?"

中国人：你的中文是[在哪里]学的？ indicates the question is asking 'where' or 'from what source'

中国人：你的中文是[怎么]学的？ indicates the question is asking 'how'

中国人：你的中文是[从哪里]学的？ indicates the question is asking 'from what source' And sources include locations and objects'-- For example: from books, from classes, from T.V. or even from my father's one on one teaching. And that's in effect, asking 'with what methods'--> 'how' you learn Chinese

When the Chinese person asking '在哪里学的':

'哪里' can refer to 'what location' e.g. Hong Kong, Beijing, Shanghai.

'哪里' can refer to 'source' e.g. books, classes, the internet.

Does 「你的中文是在哪里学的？」mean “How did you study Chinese?” or “Where did you study Chinese?”

It can mean either.

在北京语言大学学的。 or 在(北京大学的)語文班学的 are both valid answers

北京语言大学 is a location, 語文班 is a source (you could have attended classes in different countries)

You didn't misunderstand the question, the questioner just didn't make his question clear if he meant to ask "how" (with what method --> from what source)

Edit:

中国人：你的中文是[在哪里]学的？ indicates the question is asking 'where'

中国人：你的中文是[怎么]学的？ indicates the question is asking 'how'

中国人：你的中文是[从哪里]学的？ indicates the question is asking 'from what source' And sources are not locations -- For example: from books, from classes, from T.V.

'From what source' = 'with what methods'  --> 'how' you learn

When the Chinese person asked '在哪里学的' but claim he was asking "how" he should have said 从哪里 instead of 在哪里

'在哪里' refers to 'what location' e.g. Hong Kong, Beijing, Shanghai.

'从哪里' refers to 'source' e.g. books, classes, the internet.

Does 「你的中文是在哪里学的？」mean “How did you study Chinese?” or “Where did you study Chinese?”

It means “Where did you study Chinese?"

中国人：你的中文是[在哪里]学的？ indicates the question is asking 'where' or 'from what source'

中国人：你的中文是[怎么]学的？ indicates the question is asking 'how'

中国人：你的中文是[从哪里]学的？ indicates the question is asking 'from what source' And sources include locations and objects'-- For example: from books, from classes, from T.V. or even from my father's one on one teaching. And that's in effect, asking 'with what methods'--> 'how' you learn Chinese

When the Chinese person asking '在哪里学的':

'哪里' can refer to 'what location' e.g. Hong Kong, Beijing, Shanghai.

'哪里' can refer to 'source' e.g. books, classes, the internet.

Does 「你的中文是在哪里学的？」mean “How did you study Chinese?” or “Where did you study Chinese?”

It can mean either.

在北京语言大学学的。 or 在(北京大学的)語文班学的 are both valid answers

北京语言大学 is a location, 語文班 is a source (you could have attended classes in different countries)

中国人：你的中文是[在哪里]学的？ indicates the question is asking 'where' or 'from what source'

中国人：你的中文是[怎么]学的？ indicates the question is asking 'how'

中国人：你的中文是[从哪里]学的？ indicates the question is asking 'from what source' And sources include locations and objects'-- For example: from books, from classes, from T.V. or even from my father's one on one teaching. And that's in effect, asking 'with what methods'--> 'how' you learn Chinese

When the Chinese person asking '在哪里学的':

'哪里' can refer to 'what location' e.g. Hong Kong, Beijing, Shanghai.

'哪里' can refer to 'source' e.g. books, classes, the internet.

Does 「你的中文是在哪里学的？」mean “How did you study Chinese?” or “Where did you study Chinese?”

It can mean either.

在北京语言大学学的。 or 在(北京大学的)語文班学的 are both valid answers

北京语言大学 is a location, 語文班 is a source (you could have attended classes in different countries)

You didn't misunderstand the question, the questioner just didn't make his question clear if he meant to ask "how" (with what method --> from what source)