Is running safe with a ths of 6.46?

Yes: Running is fine as long as you are feeling well. Please see a physician to get the high TSH evaluated and treated.

Ask Dr. personally: As of February 2010, at most laboratories in the U.S., the official "normal" reference range for the Thyroid Stimulating Hormone (TSH) blood test runs from approximately .5 to 4.5/5.0. This was in a recent article, not 2010. So I would think that you should consult with the Dr. who determined your levels or have the test run again to compare.