For anyone unfamiliar with how "gustar" works, it literally means "to please." So this sentence literally means "Your teachers don't please you?" but in English we would say "You don't like your teachers?"
So instead of using a subject you'll use its indirect object: yo -> me, tú -> te, él/ella/usted -> le, nosotros(as) -> nos, and ellos(as)/ustedes -> les. If the thing that is liked is singular, use "gusta;" if it is plural, use "gustan." Me gusta mi maestro; me gustan mis maestros.
Also you can add "A [subject]" to the start of the sentence to be more specific. Le gusta su maestro = he/she/you likes his/her/your teacher ... very ambiguous. So we can specify "A ella le gusta su maestro" (She likes her teacher) or "A Juan le gusta su maestro" (Juan likes his teacher).
You can check out http://www.studyspanish.com/lessons/gustar.htm for further explanation and more examples.
In this component of your sentence, "No les gustan...", "Les" indicates that the subject is the plural "you" (as in "You people") or also "They". It would translate to "Do you(people) not like" or "Do they not like". "Te" is a variant of the singular "you" which functions with the translation "Do you not like..". Also, If you begin the sentence with the components "No Les gustan" you must finish it with "los maestros?" All this happens solely because the verb "gustar" modifies/conjugates with the direct object, NEVER the subject.
Me gusto a mi. - The verb was modified to "gusto" because the object pronoun, mi, is a reflexive of the 1st Person Singular; I, myself, me.
Me gustas tú. - The verb was modified to "gustas" because the direct object, tú, is the 2nd Person Singular.
Me gusta él. - The verb was modified to "gusta" because the direct object, él, is the 3rd Person Singular.
Me gustan ellos. - The verb was modified to "gustan" because the direct object, ellos, is the 1st Person Plural. Et cetera..
Hope this helps!
I know what you're trying to say, but i must clarify.
"Me gustas tú. - The verb was modified to "gustas" because the direct object, tú, is the 2nd Person Singular. " This is wrong in that the object never modifies a verb.
Me is the object. Tú is the subject.
In the English equivalent, I like you, 'I' is the subject, and 'you' is the object. So i can see what you are trying to say. However, your mislabeling of subject and object will confuse people.
The subject always modifies the verb.
The teachers please me. The teacher pleases me. The teacher and the teachers are the subjects that modify the verb. (please vs. pleases) The direct object 'me' doesn't change the verb. This logic is the same in Spanish.
Because that is the exact opposite of the real meaning.
Remember: in English the person having the feeling is the subject of a sentence with the verb like. But in Spanish, the thing causing the feeling is the subject of a sentence with the verb gustar.
So: Your teachers do not like you = no les gustas a tus maestros
Although, really, gustar isn't used so much by native speakers for the like feeling about people.
With people, better to use other phrases like agradar or caer bien, which operates similar to gustar: the people causing the feeling are the subject of the verb sentence..
You don't like your teachers = no te agradan tus maestros.
Your teachers don't like you = no les agradas a tus maestros.
Gustar has the same connotation and 'feels' the same as To Like. So if you want to translate To Like, Gustar is the best choice. However, a more literal translation (at least by grammatical construction) is To Please.
Te gustas = You please you (I'm not sure you want to say that to anyone.)
Me gusta tu maestro = Your teacher pleases me. (I like your teacher.)
Te gustan tus maestros = Your teachers please you. (You like your teachers.)
*don't forget Tu ≠ Tú
The problem is: gustar does not actually mean like.
But a Spanish speaker would use gustar to talk about a feeling that an English speaker would describe with like.
The difficulty is that the English verb and the Spanish verb work in different directions.
Like: [person having feeling] likes >>> [thing causing feeling] I like coffee.
Gustar: [thing causing feeling] gusta >>> [person having feeling] Me gusta el café.
This problem of like/gustar causes problems not only for English speakers learning Spanish but also for Spanish speakers learning English.
Which is why, when I once asked one of my Mexican students why she didn't drink coffee, she replied: "The coffee no like me."