In the sentence "They told me that they had build a new house", which option best corrects the verb form so that the reported speech is grammatically accurate?

Introduction / Context:
This sentence improvement question checks your understanding of verb forms in the past perfect tense, especially with irregular verbs. The sentence They told me that they had build a new house attempts to use the past perfect had built to describe an action completed before another past action. However, the past participle form is wrong. You must select the option that corrects this error without disturbing the meaning.

Given Data / Assumptions:

• Original sentence: They told me that they had build a new house.
• Reported speech with that suggests a prior completed action.
• The verb build is irregular: present build, past built, past participle built.
• Options: have built, have build, had built, No improvement.

Concept / Approach:
In reported speech that describes a past action completed before another past event, English uses the past perfect tense: had plus past participle. The main verb in the reporting clause is told, which is past, and the reported action building the house happened before that. Therefore the correct structure is had built. The phrase had build is incorrect because build is the base form, not the past participle. Have built would move the tense to present perfect and not match the past reporting verb told.

Step-by-Step Solution:
Step 1: Identify the two time levels in the sentence: telling happened in the past, and building the house happened even earlier.Step 2: Recall the rule that for an action completed before another past action we use past perfect: had plus past participle.Step 3: Determine the correct past participle of build, which is built, not build.Step 4: Combine had with built to form had built and fit it into the sentence: They told me that they had built a new house.Step 5: Compare with the options and see that had built (option C) is the only one that follows both the tense rule and the correct verb form.

Verification / Alternative check:
Test the other options. If you use have built, the sentence becomes They told me that they have built a new house. Mixing a past reporting verb (told) with present perfect in the subordinate clause is unusual in standard exam English; we normally backshift to had built. If you use have build or leave the sentence unchanged, the form build after a perfect auxiliary is incorrect because the auxiliary must be followed by the past participle built. This confirms that had built is the correct correction.

Why Other Options Are Wrong:
Have built uses the present perfect, which is generally used with a present context, such as They have built a new house this year. In reported speech after told, we expect a past perfect form instead. Have build is doubly wrong because both tense and verb form are incorrect. No improvement cannot be chosen since had build clearly breaks the rule of using the past participle after had.

Common Pitfalls:
Learners often forget that irregular verbs do not form their past and past participle by adding ed. Build follows the pattern build, built, built. Confusion also arises when reporting speech, especially about whether to change tenses. A good strategy is to practice common irregular verbs in all three forms and to remind yourself that when a past event is reported as having taken place before another past event, past perfect is the safest choice.

Final Answer:
The grammatically correct version of the sentence is They told me that they had built a new house, so the correct option is had built, and option C is correct.