The event occured in $2008$ but didn't occur in $2006$ and $2013 \implies x<7 $ Occured in $1986$ and $1996$ but didn't occur in $1993 \implies y<10 \implies x+y<17 $ The key observation is that if an event occurs/doesn't occur in year $k$ it also occurs\doesn't occur in year $k+x+y$. Now, by case-checking(as an example, $1976-1964=12 \implies x+y \not= 2,3,4,6,12 $) we deduce that $x+y=11$ or $x+y=13$. If $x+y=13$, the event occured in $1990$ and $1996$, hence $y<5$ which would imply $x>7$, impossible. $\implies x+y=11$. Hence the event didn't occur in $2006-11=1995$ or $1976+22=1998 \implies x<3$. The event occured in $1987$ so $x=2$. It also happened in $2007$ and hence it will first happen again in $2008+10=\boxed{2018}$