Does anyone know how to answer this?

 Yes.  The answer is:  [C]:  "1 " .

Explanation:

The equation for a line, in "slope-intercept format" , is:

                      →    y = mx + b ;

                 in which "b" = the y- intercept; or the value of 'x' when "y = 0" ; 
                               "m" = the slope; which is also the coefficient of "x". 

In "slope-intercept format", the "y" remains isolated on the left-hand side of the equation, with no "coefficient" (other than the "implied coefficient" of "1").


So, if the two particular lines are parallel, and we know that the slope is "1" for EACH line; (that is, "m = 1" for each line);  then the PRODUCT of the two slopes is:

                        →    m²   =  m * m  =  1²  =  1 * 1  =  1 .

                        →  The answer is: Answer choice: [C]:  "1" .