gcd(8,27)=1 thus there exists a unique congruence class of solutions.

8x = 1 = -26 mod(27)

Thus,

8x = -26 (mod 27)

They share a factor of 2 which is coprime with 27, divide by it.

4x = -13 = 14(mod 27)

Again divide by it,

2x = 7 (mod 27)

Again,

2x = - 20 (mod 27)

x = -10 (mod 27)

Thus,

x = 17 (mod 27)