a) (2√3 - √3 + 3).(2√2 +√3 - 3)

First, let's simplify the expression inside the parentheses:
2√3 - √3 + 3 = √3 + 3

Now, let's simplify the expression outside the parentheses:
(√3 + 3).(2√2 +√3 - 3)

Using the distributive property, we can multiply each term inside the parentheses by each term outside the parentheses:
(√3)(2√2) + (√3)(√3) + (√3)(-3) + (3)(2√2) + (3)(√3) + (3)(-3)

Simplifying each term:
2√6 + 3 + (-3√3) + 6√2 + 3√3 - 9

Combining like terms:
2√6 + 6√2 + (-3√3 + 3√3) + (3 - 9)

Simplifying further:
2√6 + 6√2 + 0 + (-6)

Final answer:
2√6 + 6√2 - 6

b) √(8 - 2√15) - √(23 - 4√15)

Let's simplify each square root expression separately:

√(8 - 2√15)
To simplify this, we need to find two numbers that multiply to give 15 and add up to -2. The numbers -5 and -3 satisfy this condition.

√(8 - 2√15) = √((√15 - 5)(√15 - 3))

Now, let's simplify the second square root expression:

√(23 - 4√15)
To simplify this, we need to find two numbers that multiply to give 15 and add up to -4. The numbers -5 and -3 satisfy this condition.

√(23 - 4√15) = √((√15 - 5)(√15 - 3))

Now, let's substitute these simplified expressions back into the original expression:

√((√15 - 5)(√15 - 3)) - √((√15 - 5)(√15 - 3))

Since both square root expressions are the same, we can simplify further:

(√15 - 5)(√15 - 3) - (√15 - 5)(√15 - 3)

Using the distributive property, we can expand each term:

(√15)(√15) - (√15)(3) - (5)(√15) + (5)(3) - (√15)(√15) + (√15)(3) + (5)(√15) - (5)(3)

Simplifying each term:
15 - 3√15 - 5√15 + 15 - 15 + 3√15 + 5√15 - 15

Combining like terms:
15 + 15 - 15 - 15 + (-3√15 + 3√15 - 5√15 + 5√15)

Simplifying further:
0

Final answer:
0