jmc

Checking the squares from $1^2$ to $10^2$, we see that no squares end in 2 or 3, while a square ends in 4 if its square root ends in 2 or 8. Since $31^2<1000<32^2$, we see that the squares less than 1000 ending in 4 are $2,8,12,18,22,28$. Thus the desired answer is $\boxed{6}$.