I use Oracle but below is how I would try it in SQL-Server:
update tablename
set fieldname = concat(substring(fieldname, 1, (length(fieldname) - 7)), 'FY16-Q1')
where fieldname like '%FY15-Q2'
It would probably be helpful to explain what I am doing in the substring()
function so here it goes:
Update fieldname to be itself but remove the unwanted 7 chars
FY15-Q2
at the end and instead concat the string with FY16-Q1