Learn French: Vous jetez le grand carton à la poubelle. - You throw the big cardboard box in the trash can.

You are thinking of the stem change! For verbs like jeter (to throw), the t is doubled when the next syllable has a silent "e", like in je jette or ils jettent. But with nous and vous, the ending makes a clear sound (-ons, -ez), so we keep the single t: vous jetez.

Why does grand come before the noun carton? I thought French adjectives went after the noun.

Most adjectives do go after the noun, but there is a common exception for short adjectives that describe Beauty, Age, Number, Goodness, and Size (often remembered by the acronym BANGS). Since grand describes Size, it goes right in front of the noun.

Why do we say à la poubelle instead of using dans (in) since the English translation says "in the trash"?

While dans does mean "inside," French uses the preposition à (which pairs with la for the feminine noun poubelle) with the verb jeter. Think of it as throwing something "to the trash" rather than "inside the trash."

Is carton exactly the same as the English word "carton"?