Please explain why the question used “molesta” instead of “molesto”.

Question

Answer

Hola Johan
In this sentence:
Me molesta que veas a ese chico. (It bothers me that you see that boy.)
The subject of the sentence is "what is bothering you" (que veas a ese chico) so verb molestar needs to agree with that; in this case, as it is an idea, we can say that "que veas a ese chico" would be "it". The verb then needs to agree with "it"which is the 3rd person singular. Let's change the sentence slightly to:
Eso me molesta. (That bothers me.)
 You can see here that:
Eso = subject 
molesta = verb (agreeing with the subject)
me = Indirect object pronoun 
All these "inverted" verbs in this lesson work the same way. The structure doesn't coincide with the English structure as in English it is a straight forward sentence with the normal order: Subject + verb + indirect object
( That + bothers + me), but in Spanish the order is inverted. 
I hope this explanation helps,
Saludos
Inma

Answer

My problem has not been addressed.  I seek clarification on why Molesta and not Molesto is used.  If it was the fact that you are seeing that boy it would the verb would be molesto as the fact “el hecho” is a masculine noun. It therefor refers to a masculine noun “el hecho” and not the female noun “la idea”.  Is the truth not then that the use of “ molesta” leaves the reader  guessing  what from a wide range of feminine verbs could be bothering the speaker?

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I think you may be thinking that verbs have a gender. Verbs don't have a gender; the -a or -o in "molesto" and "molesta" is nothing to do with masculine or feminine. It is simply the ending for a conjugation. See these examples:

1. A Antonio le molesta el ruido. (The noise is bothering Antonio.)
2. A María le molesta el ruido.  (The noise is bothering María.)

We have a male and a female, but the verb is still molesta for both. And we have a masculine noun "el ruido" but we have still molesta in both sentences.
If we change the sentences to something in feminine, for example:

1. A Antonio le molesta la manifestación. (The demonstration is bothering Antonio.)
2.  A María le molesta la manifestación. (The demonstration is bothering María.)

It is still molesta for both sentences, despite having a feminine noun (la manifestación, the demonstration) because we still have to conjugate the verb molestar with an -a at the end.
Here is a basic lesson on the verb gustar which works the same way as molestar if you want to have a look: Gustar
Saludos
Inma

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Hi Please ignore my question I have been trying to use the adjective molesto rather than the verb molestar.  I now see that such adjectival use is not viable.

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Hola,In one of the mini quizzes it says:El director les entregó un premio a los estudiantes I paused because I thought it might have to be ‘al director at the start’ ie ‘a + el director + les...’Could you clear up my doubts, please?Gracias,*ps. I’ve just realised this is ok after all, as les refers to the students. ¡Lo siento!