Learn Spanish (Latin America): Tienes que descargar el inventario y dejármelo aquí. - You have to unload the inventory and leave it for me here.

me (for me) is the indirect object pronoun, and lo (it) is the direct object pronoun referring to el inventario. When a verb is in its infinitive form (like dejar), you can attach these pronouns directly to the end of it. Remember that the indirect object always comes before the direct object.

Why is there an accent mark on the 'a' in dejármelo?

The original infinitive is pronounced with the stress on its final syllable: de-JAR. When you attach two pronouns (me and lo), you add two extra syllables, moving that stressed 'a' to the third-to-last position. Spanish spelling rules require a written accent mark to keep the spoken stress on that original vowel.

Could I move the pronouns to the front and say me lo tienes que descargar...?

You usually can place object pronouns before a conjugated verb phrase like tienes que. However, this sentence has two infinitives connected by y (descargar and dejar). Putting the pronouns at the very beginning makes it sound like they apply to descargar as well. Attaching them directly to dejar is much clearer here.

Doesn't descargar mean 'to download'?