"Fluent" is difined (in the Oxford dictionary and dictionary.com) as being able to express oneself easily and articulately. You don't need to know multiple synonyms to be able to accurately express yourself, therefor fluency happens well before 15,000, 17,000, or 20,000 words. That number also doesn't take into account the massive amount of words that have multiple meanings and can be used many different ways, for example, the word "set", which is estimated to have for 450 different uses (in English) which again, cuts down on the actual number of words you need to know in order to express yourself easily and articulately. It is estimated that only about 1,000 - 2,000 words are used in 90% of every day speaking or writing, and that a vocabulary of just 3,000 words provides a reader with with about 95% comprehension of common written texts. Let's split the difference and say 3 and 1/2 months and 2,500 words. That's only 24.04 words a day, many of which are "filler" or "connecter" words that come somewhat naturally without actually having to specifically learn them. It's absolutely achievable. Many studies have backed up this rough number, and multiple teachers and courses claim to deliver fluency in 3-4 months, not because it sounds crazy, but because it is quite achievable when the student will put in the effort. The problem with fluency is rarely the teacher or the amount time, but with the student and his or her determination. Also, I worked with Victor today and learned 11 new words in just an hour so hittin the big TWO FOUR target shouldn't be too much of a stretch... and... THAT'S all I have to say about that!

Of course Dorothy! When I say fluent, I mean you didn't make mistakes in pronunciation or in grammar, or you are not thinking in your native language and doing translation at the same time.

For example when I say ¿Cómo estás? in Spanish you understand the concept and you don't need to translate it. You're able to say it without any mistake. But all depends which is your level (A1-A2-B1-B2-C1-C2) and your age.

It's impossible to be fluent in 3 months from A1 to C2, because one level takes that time. If anyone might be able to speak Spanish as a native in 3 months, I wouldn't have a job.

I was trying to learn spanish by myself, I know many words, but it is hard for me to make a good or correct sentence, I feel so frustrated. My reading is better than my speaking. Many words that I knew when I hear them, they sound very different to me. :(

Ah - yes! With a definition of fluent like that SURE! Three months is definitely possible. You can just say the things that you know how to say well, understanding that you aren't going to understand (or be able to say) everything in 3 months. 

That definition makes all the difference. 

Thank you for you comment. Have a nice day Dorothy!