Given circles are

$x^2+y^2-4x-6y+12=0 ...\left(1\right)$

$\therefore$$c_1\equiv \left(2,3\right) \& r_1=\sqrt{4+9-12}=1\text{unit}$

& $x^2+y^2+4x-2y-4=0 ...\left(2\right)$

$c_2\equiv \left(-2,1\right) \& r_2=\sqrt{4+1+4}=3\text{units}$

Let $c$ be the internal centre of similitude, it divides $c_1{c}_2$ in the ratio $r_1:r_2$internally.

$\therefore c\equiv \left(\frac{3\times 2-2}{1+3}, \frac{3\times 3+1}{1+3}\right)\equiv \left(1,\frac{5}{2}\right)$