6cos30-3tg60+2sin45

Let's calculate the expression step by step, using the known values of the trigonometric functions:

1. cos(30°): The value is \(\frac{\sqrt{3}}{2}\).
2. tg(60°): The value is \(\sqrt{3}\).
3. sin(45°): The value is \(\frac{\sqrt{2}}{2}\).

Now plug these values into the expression:

\[ 6 \cos(30°) - 3 \tan(60°) + 2 \sin(45° \]

Substituting the values we have:

\[ = 6 \left(\frac{\sqrt{3}}{2}\right) - 3\left(\sqrt{3}\right) + 2\left(\frac{\sqrt{2}}{2}\right) \]

Now simplify each term:

1. \(6 \left(\frac{\sqrt{3}}{2}\right) = 3\sqrt{3}\)
2. \(-3(\sqrt{3}) = -3\sqrt{3}\)
3. \(2\left(\frac{\sqrt{2}}{2}\right) = \sqrt{2}\)

Putting it all together:

\[ = 3\sqrt{3} - 3\sqrt{3} + \sqrt{2} \]

The \(3\sqrt{3}\) and \(-3\sqrt{3}\) cancel each other out:

\[ = \sqrt{2} \]

Thus, the final result is:

\[ \sqrt{2} \]