the number of common tangents to the circle x² +y² =4

and the circle

x² + y² -6x-8y =24 is

x² + y² -6x - 8y =24

Circle 1 has center as (0,0) and radius 2
Circle 2 has center as (3,4 ) and radius  7

If you plot both circles , they will intersect each other.
So only two common tangents can be drawn. If they only touch each other , then there will be 3 tangents.
For two intersecting circles, there are two common tangents always.