a) \(13-18-\left(-42\right)-15\)
\(=13-18+42-15\)
\(=\left(13-18-15\right)+42\)
\(=-20+42\)
\(=22\)
b) \(369-4.\left[-5+4.\left(-8\right)\right]\)
\(=369-4.\left[-5+\left(-32\right)\right]\)
\(=369-4.\left(-37\right)\)
\(=369+148\)
\(=517\)
c) \(\left(-8\right)^3\div\left(-8\right)^2+8\)
\(=-8+8\)
\(=0\)
d) \(\left(-12\right).\left(-13\right)+13.\left(-29\right)\)
\(=12.13+13.\left(-29\right)\)
\(=13.\left(-29+12\right)\)
\(=13.\left(-17\right)\)
\(=-221\)