Let us simplify

Simplifying 1^st part by rationalizing the expression by multiplying and dividing by 2 + √2

=  = = 4√3 + 2√6

Simplifying 2^nd part by rationalizing the expression by multiplying and dividing by 4√3 + √18

=   

Simplifying 3^rd part by rationalizing the expression by multiplying and dividing by 3 + √12

= = -

Putting all values we get;

4√3 + 2√6 – (4√3 – √18) + (3√2 + √24)

4√3 + √6 × 2² – (4√3 – √18) + (√2 × 3² + √24)

4√3 + √24 – (4√3 – √18) + (√18 + √24)

= 2√24 = 4√6