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In this sentence, I do not understand the purposes of each of the 2 instances of the character 学.
我学英语学了4年了。
I have been studying English for 4 years.
In my naive understanding I would personally translate the English to Chinese as follows:
我学了英语4年。
I think this might be related to my confusion about the phrase 学英语. Is this a noun that means "The Study of English" or is it a verb like "to study English"? I can see why you might add a second 学 if the former is true.
The interesting phenomenon in this example is the use of 了。。。了 to indicate an ongoing action. In cases where the ongoing verb takes an object (like 英语 in your sentence), the verb is repeated. If the object is understood, it doesn't need to be repeated. For example, if you've established with your interlocutor that you're studying English, you might say 我学了一年了 (I have studied for a year).
As an aside, your "naive translation" would be closer to "I studied (i.e., completed studying) English ...". If this is your intent, a more apt translation might be 我学了四年英语
"我学英语" = "I learn English" -- it is the main clause
"学了4年了" = "have learned (it) for four years" -- it is the relative clause that give us additional information of 'the duration of the action' .
"我学英语学了4年了" = "I learn English, and I have learned it for four years"
Repeat the verb in the relative clause that state the duration of the action is a common structure in Chinese. It put emphasis on the duration.
Example:
我吃了飯 (I've eaten dinner)
我吃了一小時飯 (I have eaten dinner for one hour)
我吃飯吃了一小時 (I ate dinner, have eaten for one hour) -- Repeat the verb in the emphasis on the duration
Both "我吃了一小時飯" and "我吃飯吃了一小時" mean "I ate dinner for one hour" the difference is the former is a plain SVO sentence that doesn't emphasize anything and the latter emphasize the duration (一小時) which becomes more important in the sentence
Similarly
我吃了飯 (I've eaten dinner)
我吃了十碗飯 (I've eaten ten bowls of rice)
我吃飯吃了十碗 ( I ate rice and I ate ten bowls of it) -- emphasize the quantity
我学英语学了4年了.
This kind of repetition is used for the extent complement. The intention is to make the complement remarkable so that the interlocutor can easily get the point that has been made.
我学英语学了4年 VS 我学了4年英语
The former is clear that the point you are trying to make is 学了4年. The latter can be understood differently depending on the emphasis you put. If you put emphasis on 4年, then it will have the same effect as the first sentence. If you put emphasis on 英语, then you are saying you've studied English for 4 years instead of other subjects such as Chinese.
This usage can be more flexible as in:
我说话说得嘴都肿了！
我跑步跑得腿都断了！
我打球打得精疲力尽！
