Hay has density = 92 kg/m^3

Manure and hay has density = 248 kg/m^3

Given 1 m^3 of hay, you will have 92 kg of hay.

Given 1 m^3 of manure and hay, you will have 248 kg of manure and hay, of which, a third is the mass of hay and 2 thirds is the mass of manure, which gives 82.7 kg of hay and 165.3 kg of manure.

Find the volume of the hay in the manure/hay mixture, using the mass of hay and it's density, and get the volume of manure.

You will get the density of manure using the values you just got.