Ineed some sentence examples on how to use the "personal a" grammar rule in spanish. i just need to clarify on when and when not to use this grammar rule.

Transitive verbs need a direct object to complete their meaning. In Spanish when the direct object of the sentence is a human being, an "a" preposition must be inserted between the verb and the direct object. The "personal a" is used exactly the same whether it is a person or several people.

Yo veo a mis hermanos.

I see my brothers.

When the direct object is a person, but the person’s title begins with "el", you can contract "a + el" to make "al". For example:

Veo a el profesor. => Veo al profesor. (masculine noun)

I see the teacher.

Since “the teacher” is "el profesor", "a + el" can contract to form "al".

On the other hand, when the direct object is a feminine noun with the "la" article, there’s no need to form a contraction.

Veo a la profesora. (feminine noun)

I see the teacher.

Yo visito a mi abuela. (direct object = mi abuela)

I visit my grandmother.

For an English speaker, this "personal a" seems unnecessary, but it is very important in correct Spanish.

The Spanish preposition "a" has a few different uses. Frequently, it’s used like the English preposition “to”.

Yo voy a la montaña. (intransitive verb, not a direct object)

I go to the mountain.

Here, we’re not using the personal "a". We’re simply using the preposition a, meaning “to”

When the direct object of the sentence is not a human being, in Spanish is not used the "personal a". Compare these sentences:

Yo visito a mi abuela. (human being)

I visit my grandmother.

Yo visito París. (not a human being)

I visit Paris.

Yo veo a una mujer. (human being)

I see a woman.

Yo veo un coche. (not a human being)

I see a car.

Since the direct object is not a human being (Paris, car), there’s no need for the "personal  a". There is only an indefinite article.