Don't really get what you mean exactly by check for H6 <>
what is <>
in your description? The exact values, a hint to a possible string interpolation?
If understood your question correctly, you can basically:
=IF(F6="YES", EDATE(B6,3),
IF(F6="NO", EDATE(H6,3),
IF(F6="MAYBE", EDATE(B6,6),
IF(F6="UNKNOWN", EDATE(H6,6),
"[Error]: Invalid Condition")
)
)
)