Verified answer

Remember that multiplication is commutative and associative.

Commutative: a×b = b×a

Associative: (ab)c = a(bc)

when you put those two facts together it means you can rearrange the terms in a multiplicative expression however you want to. Let's look at your example (I'm going to use a^n to mean "a" raised to the power n)

3(x^3)(y^2)(6(x^2))

now, using the power of the commutative and associative laws, I'm going to move all the constant terms to the far left:

(3)(6)(x^3)(y^2)(x^2)

multiplying the 3 and 6 give me

18(x^3)(y^2)(x^2)

Now let me swap the order of the y^2 and the x^2 terms (commutative law)

18(x^3)(x^2)(y^2)

Now use the rule that (a^n)(a^m) = a^(n+m) to simplify the x terms

18(x^(3+2))(y^2)

18(x^5)(y^2)

first numbers times numbers result in numbers...

5 * 4 = 20

6* 3 = 18

next exponents means that you mult. the same item by itsel.

x* x = x^2

here is the main point

look at x^2 * x^ 2

x^2 = x*x

so x^2 * x^ 2 is he same as x*x*x*x .. or x^4

notice that the exponents add x^n * x^m = x^n+m

3x³y² (6x²)= is the same as 3*6 x^3 * x^2 y^2

6*3 = 18

x^3*x^2 = x^5

y^2 = y^2

string them together:18x⁵y²

If a bunch of terms are multiplied together, you can rearrange the order

as much as you like.

And x^3 = x*x*x etc.

So

3x³y² (6x²)

you can multiply 3 * 6 = 18

x^3 * x^2 = xxx * xx = xxxxx = x^5

and y^2 stays y^2

3x³y²(6x²) = 3·6·x³·x²·y²  commutative property of multiplication

     = 18x³⁺²y²   

     = 18x⁵y²