The correct answer for is A.
Translation:
Wǒ míngtiān bānjiā, nǐ yǒukòng ma?
Jack：我 明天 搬家，你 有空 吗？
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I’m moving to the suburbs tomorrow, are you free?
Yǒukòng, wǒ qù bāng nǐ ba.
Tony：有空， 我 去 帮 你 吧。
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I’m free. I’ll go help you out.
Explanation:
Both 帮 (bāng) and 帮忙 (bāngmáng) have to do with help, but they differ in the following ways:
1. 帮忙 (bāngmáng)
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a. Used as a noun.
Wǒ xūyào nǐ de bāngmáng.
我 需要 你 的 帮忙。
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I need your help.
b. Used as a verb. When the word 帮忙 (bāngmáng) is used as a verb, the structure is: 帮忙 (bāngmáng) + V + Object.
Qǐng bāngmáng jiějué yíge wèntí.
请 帮忙 解决 一个 问题。
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Please help me solve the problem.
Note: 解决(jiějué) is the verb and 一个问题 (yíge wèntí) is the object.
Guòlái! Bāngmáng bān jiājù.
过来！ 帮忙 搬 家具。
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Come here! Help move the furniture.
Note: 搬 (bān) is the verb and 家具 (jiājù) is the object.
c. Used as a verb 帮 (bāng, help) and noun 忙 (máng,favor). Place words between 帮 (bāng) and 忙 (máng), such as the measure word 个 (gè). 帮个忙 (bāng ge máng), meaning “to do somebody a favor.”
Wǒ qǐng nǐ bāng ge máng.
我 请 你 帮 个 忙。
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I would like you to lend me a hand.
2. 帮 (bāng)
It can only be used as verb when meaning “help” with the structure of 帮 (bāng) + sb + do something. In some oral situations the direct object will be omitted. In the above conversation, Tony says, “我去帮你吧。(Wǒ qù bāng nǐ ba.)” In this sentence, the object is omitted.
Examples:
Qǐng bāng wǒ xiě yìfēng xìn.
请 帮 我 写 一封 信。
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Please help me write a letter.
