How to allocate memory to a struct in a function ?

The memory allocation call is correct but the assignment is wrong. By starting the line with the type Activity* you are telling the compiler to create a local variable with the name specified after the type. But that name is invalid because it contains unallowed characters and you probably don't want to create a local variable but assign the allocated memory to the passed structure.

If you have the address *sys of an existing RoomSystem structure:

sys->c_array = malloc(num_challenges * sizeof(Activity));

If you have a function with a RoomSystem **sys parameter:

Result create_system(RoomSystem **sys)
{
    *sys->c_array = malloc(num_challenges * sizeof(Activity));
    /* Assuming RESULT_* are Result values */
    return (*sys->c_array == NULL) ? RESULT_NO_MEM : RESULT_OK;
}

Activity *temp = malloc(num_challenges * sizeof(Activity));
*sys->c_array = temp;