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I am trying to learn Spanish and I am stuck in understanding the following.
"Mucho gusto" means, "nice to meet you".
However, "muchas gracias" means, "thank you very much".
I know that "muchas" is plural and feminine and "mucho" is singular and masculine, but how does "mucho" in "mucho gusto" become "nice to meet you" but the "muchas" in "muchas gracias" becomes "thank you very much", i.e. "muchas" becomes "very much" and "mucho" becomes not even sure what it means in "mucho gusto".
You shouldn't try to learn another language based on translations. Your are not automatic translation software, so you'd better try to understand the underlying meaning of the original words instead. So let's see what "mucho" and "gusto" mean:
Mucho: "Numeroso, abundante, intenso."
Gusto: "Placer o deleite."
So we have "mucho" equals "a great amount" and "gusto" equals "pleasure". So "mucho gusto" equals "un gran placer" or, as you say in English, "a great pleasure".
Answering your question, there's no difference between "mucho" and "muchas" beyond the use of the masculine/feminine and singular/plural to match the noun it affects ("gusto" or "gracias"). In both cases it means "a great amount" or "abundant" or "above the standard amount":
"Muchas gracias": My gratitude is above the standard amount.
"Mucho gusto": My pleasure to meet you is above the standard amount.
Your confusion with the translation of "mucho gusto" as "nice to meet you" is that the word "mucho" is not translated. You have translated "gusto en conocerte" instead. Maybe a more accurate but not idiomatic translation would have been "It's very nice [to meet you]", so there you have the word "very" that maybe helps you with understanding the word "mucho".
The problem is that you are comparing equivalent sentences that are not exact translations of each other.
Mucho gusto does not translate nice to meet you but it is equivalent.
The full sentence would be Me da mucho gusto en conocerte which would be I feel very pleased on meeting you. Here mucho is very
In the other example muchas gracias does mean thank you VERY much where again muchas is very.
So now you can see that in both cases mucho, mucha means very for masculine and feminine respectively and muchos, muchas are the same but for the plural.
In general mucho means a lot, very, much
