Question 9656
First, you need to recognise this as the difference of two squares, and this factors like:

{{{a^2-b^2 = (a+b)(a-b)}}}

{{{81x^4 - 16 = (9x^2 - 4)(9x^2 + 4)}}}

Again, you have the difference of two squares, so this will factor.

{{{(3x-2)(3x+2)(9x^2+4)}}}

If you really want to factor completely, the the sum of two squares can be factored: {{{(a^2 + b^2) = (a - bi)(a + bi)}}} where: {{{ i = sqrt(-1)}}}

The complete factorisation then is: {{{(3x-2)(3x+2)(3x-2i)(3x+2i)}}}

If you are not yet into complex numbers, then leave it at: {{{(3x-2)(3x+2)(9x^2+4)}}}