The nine shaded cells form a $3\times 3$ block of dates whose sum is 117. What is the date in the bottom-right cell of the block?

In a $3\times 3$ block the dates are symmetric about the centre $c$, so their sum is $9c=117$ and $c=13$. The bottom-right cell is one row down (+7) and one column right (+1): 13 + 8 = 21. (13 is the centre; 19 is the bottom-left.)