The circles x^2+y^2=16 and x^2+y^2-6x-8y+9=0 have exactly how many common tangents?

The first circle has centre $(0,0)$ and radius $4$. The second has centre $(3,4)$ and radius $\sqrt{9+16-9}=4$. The distance between the centres is $5$, which lies between $|4-4|=0$ and $4+4=8$, so the circles intersect at two points and have exactly $2$ common tangents. Four tangents need disjoint circles; three need external touching.