[cvc121]

When naming an organic compound with more than 1 alkyl group, how do you know which to put first when naming it? For example, 3-ethyl-2,4-dimethylhexane? Could it also be written as 2,4-dimethyl-2ethylhexane?

[discodermolide]

The substituents are placed in alphabetical order. i.e. dimethyl before ethyl.
The numbering is arranged so that the sum of the numbers is lowest i.e. in your example 3-,2,4- = 9 or 2,4-2- = 8. Therefore the latter is correct, 2,4-dimethyl-2-ethylhexane.

[mjc123]

Those are different compounds, aren't they? 2-methyl-2-ethyl implies a quaternary carbon, while 2,4,3- implies three tertiary carbons. Besides, you can't have a 2-ethyl alkane - by definition you aren't basing it on the longest chain. "2,4-dimethyl-2-ethylhexane" is 3,3,5-trimethylheptane.