I found a good discussion about using muito here:
Basically, the two rules to remember are:
1- If the word “muito” is followed by an adjective, then the word does not vary. If it is followed by a noun, then it will change.
2 - When you are talking about degree (when the translation is very) never change the word. When you are talking about quantity (when the translation is many or a lot of) you have to vary it according to the word that comes after.
I hope this helps you!