Factor, not "solve".  "Solve" means to find the numerical values of the
variables, which is not possible when you only have an expression and
not an equation.  So we will factor this:

81x² - 72xy + 16y²

Since the first term and last term are both perfect squares,
of 9x and 4y try this factorization:

(9x   4y)(9x   4y)

Then you can see there would have to be a - sign in each, so
the factorization becomes:

(9x - 4y)(9x - 4y)

and since those factors are the same, we can simplify by writing
it as

(9x - 4y)²

That's the final answer.  Notice you didn't "solve" anything because
you still don't know any particular value that x must equal or that y 
must equal.  You factored the expression, but you didn't "solve"
anything.

Edwin