Correct, you figured it out.
For an alkane;
1) find the parent molecule (longest continuous chain)
2) find the first substitute
3) begin numbering from this side of the parent
4) put into alphabetical order
On a side note though, shouldn't it be 8-ethyl-2,6-dimethyl-4-isopropyldecane or am I incorrect recalling that prefixes (iso, sec, tert) do not get involved in the order? The correct answer above follows ethyl, isopropyl, methyl not ethyl, methyl, isopropyl alphabetic order.