Beta oxidation would proceed normally, up until it produced a *cis-∆3,∆6 fatty acid*.
The cis-∆3,∆6 fatty acid would at this point be converted to a *trans-∆2 cis-∆6 fatty acid* by *∆3,∆2-enoyl-CoA isomerase*
The trans-∆2 cis-∆6 fatty acid is a substrate for the normal hydratase enzyme in step 2 of beta oxidation (enoyl-CoA hydratase).
This beta oxidation cycle then proceeds normally, leaving a cis-∆4 fatty acid.
In the next cycle:
With a cis-∆4 FA substrate, acyl-CoA dehydrogenase produces a trans-∆2 cis-∆4 fatty acid.
The resulting *conjugated* double bond cannot be hydrated by enoyl-CoA hydratase --> instead, it is reduced by *2,4-dienoyl-CoA reductase*, yielding a trans-∆3 fatty acid.
The trans-∆3 fatty acid is then converted to a trans-∆2 fatty acid by *∆3,∆2-enoyl-CoA isomerase*.
After this, beta oxidation proceeds normally.