6.6.23 Combinatorics

Problem: Find the coefficients when \[ a=x^{2} \cdot y^{4} \cdot z^{6}, b=x^{2} \cdot y^{2} \cdot z^{2}, c=x^{2} \cdot y^{8} \] in the expansion \( \left(4 \cdot x+5 \cdot y^{2}+z^{3}\right)^{6} \).