The depreciation of 10% means that the machine is worth 90% of its previous year's value. After 4 years the depreciation is 0.9^4=0.6561, so applying this to $3,000=$1,968.30.
After a further 2 years this comes to $1,594.32.
The depreciation to $1,046 is 1046/3000=0.34867 approx. To find out how many years this is, we need logarithms: x=log0.34867/log0.9=10 years.