1. The problem asks to factorise completely the quadratic expression $$9x^2 - 4$$. 2. Notice this is a difference of squares, which has the general formula $$a^2 - b^2 = (a-b)(a+b)$$. 3. Here, identify $$a = 3x$$ because $$9x^2 = (3x)^2$$ and $$b = 2$$ because $$4 = 2^2$$. 4. Applying the difference of squares formula: $$9x^2 - 4 = (3x - 2)(3x + 2)$$. 5. This is the completely factorised form of the expression. Final answer: $$(3x - 2)(3x + 2)$$.