Final answer:
The sentence is grammatically incorrect because the verb 'trabajar' was not correctly conjugated.
Step-by-step explanation:
The sentence "Quiero trabajo mucho en la casa." is grammatically incorrect. The correct sentence would be "Quiero trabajar mucho en la casa." In Spanish, the verb "trabajar" (to work) needs to be conjugated to match the subject, which in this case is "yo" (I).
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