(2sqrt (3)cdot sqrt (2))/(sqrt (6))+3cdot sqrt ((1)/(9))=

To simplify the expression, we can start by simplifying the numerator and denominator separately.<br /><br />In the numerator, we have $2\sqrt{3} \cdot \sqrt{2}$. We can multiply the square roots together to get $2\sqrt{6}$.<br /><br />In the denominator, we have $\sqrt{6}$.<br /><br />Now, we can simplify the fraction by dividing the numerator by the denominator:<br /><br />$\frac{2\sqrt{6}}{\sqrt{6}} = 2$<br /><br />Next, we can simplify the second term in the expression, which is $3 \cdot \sqrt{\frac{1}{9}}$. We can take the square root of $\frac{1}{9}$ to get $\frac{1}{3}$, and then multiply it by 3 to get 1.<br /><br />So, the final simplified expression is:<br /><br />$2 + 1 = 3$<br /><br />Therefore, the answer is 3.