Chapter 1: Maintaining the Supply Chain  

Slóthi is worried that when the Orcs attack, the dwarves might be cut off from the outside world and will not survive a long siege.

Talk to Thórgnyr

Thórgnyr is outside Moria by the Doors of Durin before the still pool.

Slóthi wants to ensure that the supply route outside Moria remains open and that there is enough food within the mines for the dwarves to survive a long siege.

Bring food supplies to Slóthi

Slóthi is in the Chamber of the Crossroads, at the southern entrance of Durin's Way, north of the Great Delving.

Thórgnyr has given you the first of several food deliveries for Slóthi, who can be found in the Chamber of the Crossroads.

We know, Thórgnyr is in The Flaming Deep, but apparently he is also outside Durin's Door in The Walls of Moria by The Black Pool.