the product of the values of a for which |5a-4|=a is true is

Solve for a over the real numbers:
abs(5 a - 4) = a

Split the equation into two possible cases:
5 a - 4 = a or 5 a - 4 = -a

Subtract a - 4 from both sides:
4 a = 4 or 5 a - 4 = -a

Divide both sides by 4:
a = 1 or 5 a - 4 = -a

Add a + 4 to both sides:
a = 1 or 6 a = 4

Divide both sides by 6:
a = 1        or          a = 2/3     Their product is simply: 1 x 2/3 =2/3