You could try a formula like this to get the last occurence
=EDATE(A2,FLOOR(DATEDIF(A2,TODAY(),"m"),6))
assuming your start date in A2......and for next occurence
=EDATE(A2,FLOOR(DATEDIF(A2,TODAY(),"m"),6)+6)
If you always want the result to be a weekday try these versions
=WORKDAY(EDATE(A2,FLOOR(DATEDIF(A2,TODAY(),"m"),6))-1,1)
....and
=WORKDAY(EDATE(A2,FLOOR(DATEDIF(A2,TODAY(),"m"),6)+6)-1,1)
You might have to check what results you get when today is exactly on the "anniversary" date, do you want today to count as the last one....or the next one?