The correct answer is option 'C' - "is washing".

Explanation:

Subject-Verb Agreement:
In English grammar, it is important to ensure that the subject and verb agree in number. This means that if the subject is singular, the verb should also be singular, and if the subject is plural, the verb should also be plural.

In this sentence, the subject is "she," which is a third-person singular pronoun. Therefore, the verb that follows should be in the third-person singular form.

Present Continuous Tense:
The verb tense used in the sentence indicates an ongoing action in the present. The present continuous tense is formed by using the present tense of the verb "to be" (am, is, are) followed by the present participle (-ing form) of the main verb.

Use of "is washing":
Option 'C' - "is washing" is the correct answer because it follows the subject-verb agreement rule and uses the present continuous tense correctly.

Here, "is" is the present tense of the verb "to be" used with the third-person singular subject pronoun "she." "Washing" is the present participle form of the verb "wash," indicating an ongoing action in the present.

Therefore, the correct sentence is "She is washing her clothes."

Incorrect options:
- Option 'A' - "wash" is incorrect because it does not agree with the subject "she."
- Option 'B' - "washing" is incorrect because it does not agree with the singular subject "she."
- Option 'D' - "are washing" is incorrect because it uses the plural form of the verb "to be" which does not agree with the singular subject "she."

Summary:
To summarize, the correct sentence is "She is washing her clothes" because it follows the subject-verb agreement rule and uses the present continuous tense correctly. The verb "is washing" agrees with the singular subject "she" and indicates an ongoing action in the present.