Learn Spanish (Spain): No tengo mucho tiempo libre.

In Spanish, words that measure amount or quantity like mucho (much) go before the noun. Descriptive words like libre (free) usually go after the noun, which is the opposite of English.

Why do we use mucho instead of mucha or muchos here?

Mucho has to match the word it describes. Since tiempo is masculine and singular, we use the masculine singular form, mucho.

I thought tiempo meant 'weather'. How do I know when it means 'time'?

Context! Tiempo is a word that means both 'time' and 'weather' in Spanish. Because we are talking about having something libre (free) and using the verb tener (to have), it clearly means 'free time' here.