Equations of circles are

\( \Large x^{2}+y^{2}+2nx+6y+1=0 \)

and \( \Large x^{2}+y^{2}+4x+2y=0 \)

Since, the circles cut orthogonally

\( \Large \therefore\ 2gg+2ff = c+c \)

=> \( \Large 2n \times 2+6 \times 1 = 1+0 \)

=> \( \Large 4h+6 = 1 \)

=> \( \Large n = \frac{-5}{4} \)