The correct answer for is A.
Wǒ míngtiān bānjiā, nǐ yǒukòng ma?
I’m moving to the suburbs tomorrow, are you free?
Yǒukòng, wǒ qù bāng nǐ ba.
I’m free. I’ll go help you out.
Both 帮 (bāng) and 帮忙 (bāngmáng) have to do with help, but they differ in the following ways:
Wǒ xūyào nǐ de bāngmáng.
I need your help.
Qǐng bāngmáng jiějué yíge wèntí.
Please help me solve the problem.
解决(jiějué) is the verb and 一个问题 (yíge wèntí) is the object.
Guòlái! Bāngmáng bān jiājù.
Come here! Help move the furniture.
搬 (bān) is the verb and 家具 (jiājù) is the object.
I would like you to lend me a hand.
It can only be used as verb when meaning “help” with the structure of 帮 (bāng) + sb + do something.
Qǐng bāng wǒ xiě yìfēng xìn.
Please help me write a letter.