The number of common tangents to the circles  

$x^2+y^2-4x-6y-12=0\text{ and }{x}^2+y^2+6x+18y+26=0$ is 

The circles can be written as 

$(x-2{)}^2+(y-3{)}^2=25$  with centre $C_1$(2, 3) and $r_1=5$

and $(x+3{)}^2+(y+9{)}^2=64$ with centrec  $C_2$(-3, -9) and $r_2=8$

$O_1{O}_2$= distance between centres 

$=\sqrt{5^2+{12}^2}=13$

as $r_1+r_2=O_1{O}_2$ 

We have that circle touch each other externally, so there are three common tangents as shown