the "de" after "pas" is used when you are expressing, e.g., that you don't have something of something. For example:
Il n'y a plus de sucre. -- There is no more (of) sugar.Elle ne boit pas d'alcool. -- She drinks not of the alcohol. (literally)
But in the example you quote, "Ils ne parlent pas l'espagnol." There is no larger thing of which the language Spanish would be part of. It is an indivisible entity. Hence no "de".
-- Chris (not a native speaker).
Bonjour Jocelyn !
To complete Chris's answer, only partitive articles (du, de la, de l', des) and indefinite articles (un, une, des) become de or d' in a negative sentence.
It doesn't apply to definite articles (le, la, l', les) or zero articles, hence:
Have a look at our related lessons:
Bonne journée !
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