what is the square root of 6x multiplied by the sqare root of 3x squared

When you multiply 2 "square root expressions", you can put the multiplication problem under 1 square root. So,

√(6x) * √(3x^{2}) = √(6x)*(3x^{2})

Follow the normal rules to multiply the expression under the square root,

√(18x^{3})

Now put this expression in simple radical form, if required, which means factoring out all the "perfect squares" from under the square root.

Factor 18 into 9*2 because 9 is a perfect square (3*3)

Factor x^{3} into x^{2} * x because x^{2} is a perfect square

√18x^{3} = √(9x^{2} * 2x) = √9x^{2} * √2x

√9x^{2} = 3x (because 3*3=9, x*x = x^{2}, so 3x * 3x = 9x^{2})

√9x^{2} * √2x = 3x * √2x, which can also be written
**3x√2x**