The correct answer is: Â [A]: Â "Â 1(x) = 1Â " .Â
          →  { that is:  " 1 *(x)  =  1 " . } .
Explanation:
Note:
The question asks:
Which of the following statements is always false when:
          →   " x = 3 " ,  " y = 2 " ,  and:  " z = 4 " ?Â
with the following answer choices:
 [A]:  " 1* (x) = 1 " ;
 [B]:  " 0 * (x) = 0 " .
 [C]:  " x + y = y + x " ;
 [D]:  " x(y + z) = xy + xz " .
 →  Let us consider each answer choice; and plug in the known values:
Â
Choice: Â [A]: Â " 1* (x) = 1Â "Â ; Â
Note: Â We are given: " x = 3 " ; Â so; plug in "3" and solve:
          →  1(3) = " 3 ";  and " 3 ≠1 " .
Furthermore: Â Given: Â " 1(x) = 1 " ; in the answer choice ;
Note that, on the "left-hand side" of the equation:
   Â
          →  1(x) = 1 * x  = x * 1 = "x" ; Â
                   Â
          →  since "any value" ; multiplied by "1" ; equals that same value.
→ As such, substitute: "x" (in lieu of "1x") ; on the "left-hand side" of the equation ;  and:
Â
→  REWRITE the equation:
        →  " x = 1 " ;Â
        →  Since we are given:  "x = 3"  ; substitute "3" for "x" in the equation, as follows:
        →  " 3 = 1 " ;  which is INCORRECT;Â
         →  since:  " 3 ≠1 " .
→ This answer is ALWAYS false;  so:
Answer choice: Â [A]: Â " 1(x) = 1 " ; should be CORRECT.
Choice: Â [B]: Â " 0 * (x) = 0 " ;
Note: Â We are given: Â " x = 3 " ; Â so; plug in "3" and solve:
          →  0(3) = 0 ;  which is: "true" in this case.
→ As such, this answer is NOT "always false" ;
→ and:  Answer choice:  [B]:  is INCORRECT.
Choice: Â [C]: Â "Â x + y = y + x " ;Â
Note: Â We are given: Â " x = 3 " ; Â AND: Â " y = 2 " ;
So plug in these given values into the equation:
           →  3 + 2 = 2 + 3 ;Â
           →  5 = 5.  Yes!Â
         Â
→ As such, this answer is NOT "always false" ;Â
→ and:  Answer choice:  [C]:  is INCORRECT.
Choice: Â [D]: Â "Â x(y + z) = xy + xz " ;Â
Note: Â We are given: Â "Â x = 3 " ;Â Â " y = 2 " ; AND:Â Â " z = 4 " ;Â
So plug in these given values into the equation:
           →  3(2 + 4) = (3*2) + (3*4)  ;Â
          →. 3(6) = 6 + 12 ;
         Â
           →  18 = 18.  Yes! Â
         Â
→ As such, this answer is NOT "always false" ;Â
→ and:  Answer choice:  [D]:  is INCORRECT.
So; the correct answer is:Â
Answer choice: Â [A]: Â " 1(x) = 1 " .Â
          →  { that is:  " 1 *(x)  =  1 " . } .
 Hope this answer—and lengthy explanation—helps!Â
 Best wishes in the community—and in your academic pursuits!