Based on the context of the problem, I assume that these triangles and parallelograms are separate shapes / areas / figures

that are located at totally different parts of the art piece and do not intersect each other and do not have common

sides and/or vertices.


Then from the condition, you have this system of equations for the number of triangles T and the number of parallelograms  P


     T +  P =  42     (1)    (counting shapes altogether)

    3T + 4P = 150     (2)    (counting sides)


To solve the system, express  T = 42 - P  from equation (1) and substitute it into equation (2), replacing T there


    3*(42-P) + 4Q = 150.


Simplify step by step


    126 - 3P + 4P = 150

     P = 150 - 126 = 24.


ANSWER.  There are 24 parallelograms and 42-24 = 18 triangles in the art piece.


CHECK.   4*24 + 18*3 = 150,  the total number of sides.   ! Precisely correct !