1) Change the arrangement and re-record the track. This is probably the least desirable solution, but it's the best way to resolve any instrument clashing. Clashes usually happen because of an arrangement problem, and changing the part that the offending instrument plays or changing the sound will save the day. The only problem is the time and effort it takes to do so.
2) Mute one of the offending instruments so that they both never play at the same time. In this case, you're changing the arrangement with the mute button by only allowing one instrument to play at a time. This actually works very well as it simplifies both the arrangement and the mix.
3) Lower the level of the offending instrument. Both instruments can't live at the same volume, but sometimes it works if one is softer than the other volume-wise.
4) Tailor the EQ so that the offending instrument takes up a different frequency space. This is usually what most engineers do and why they get paid the big bucks (chuckle). By carving out a separate frequency area for each instrument, both can live together at the same volume.
5) Pan the offending instrument to a different location. Sometimes this works surprisingly well. By just moving one of the instruments a little in the stereo field, both instruments can have their own space. Many times guitars that clash with suddenly work together if they're panned wide left and right, but sometimes only a hair will work too.
The next time you have a problem with a couple of instruments clashing, remember this post. One of the 5 tips will always work.
Don't forget to check out my Music 3.0 blog for tips and tricks on navigating the music business.