Evaluating a Rational Expression

Very Hard Algebra Expressions, Equations, And Inequalities

Let $$x$$ be a real number such that $$x^2 - 6x + 8 = 0$$. Suppose we define a new variable $$y$$ such that $$y = 3 +\frac{4}{x - 2}$$. What is the value of $$y$$ when $$x$$ takes on its larger solution?

$$5$$