Answer
$Z=18\ g/mol$
$A=26\ g/mol$
Work Step by Step
Molar masses:
$A_2Z_3:\ 15.9\ g\div0.15\ mol=106\ g/mol$
$AZ_2:\ 9.3\ g\div0.15\ mol=62\ g/mol$
$62=A+2\times Z\rightarrow A=62-2\times Z$
$106=2\times A+3\times Z$
$106=2\times (62-2\times Z)+3\times Z$
$Z=18\ g/mol$
$A=26\ g/mol$