The seven values 12, 15, 15, 18, 21, 24 and $x$ have the same mean, median and mode. What is $x$?

The mode is 15 (unless $x$ creates a tie, which would give two modes). For the median also to be 15, $x$ must not exceed 15, making 15 the 4th value. Then mean $=\frac{105+x}{7}=15\Rightarrow x=0$. Check: 0, 12, 15, 15, 18, 21, 24 has mean, median and mode all 15.