\(a,13-18-\left(-42\right)-15\)
\(=13-18+42-15\)
\(=\left(13-15\right)-\left(18+42\right)\)
\(=-2-60\)
\(=-62\)
\(b,369-4\left[\left(-5\right)+4.\left(-8\right)\right]\)
\(=369-4\left[\left(-5\right)+\left(-32\right)\right]\)
\(=369-4.\left(-37\right)\)
\(=369-\left(-148\right)\)
\(=369+148\)
\(=517\)
\(c,\left(-8\right)^3:\left(-8\right)^2+8\)
\(=-512:64+8\)
\(=-8+8\)
\(=0\)
\(d,\left(-12\right)\left(-13\right)+13.\left(-29\right)\)
\(=156+-377\)
\(=156-377\)
\(=-221\)