Excellent work anon :)

 

$$\left({\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\left(-{\mathtt{5}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}\left({\mathtt{2}}{\mathtt{\,-\,}}\left({\mathtt{3}}\right)\right){\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right){\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,-\,}}\left({\mathtt{2}}\right) = -{\mathtt{44}}$$

Don't forget the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

 

In the case of

(4+2(-5)+3(2+(-3))+2)6+(-2),

which should be written as 6[4+2(-5)+3(2+[-3])+2]+(-2),

First:

6[4+2(-5)+3(2+[-3])+2]+(-2) --> The bolded terms can become 2-3, which is -1. You are doing the parentheses first, and that is the smallest parentheses term you can simplify.

 

Now you have 6[4+2(-5)+3(-1)+2]+(-2).

Continue inside the parentheses, but now with multiplication (in this case you're doing the order of operations within the order of operations!):

6[4+2(-5)+3(-1)+2]+(-2) --> The bolded areas are 2 x -5, which becomes -10; and 3 x -1, which becomes -3.

You now have: 6[4+(-10)+(-3)+2]+(-2)

You should never have something plus a negative, because that can simplify to minus a positive.

You now have: 6[4-10-3+2]-2

Simply complete the addition or subtraction within the parentheses in the order it is shown from left to right:

6[-6-3+2]-2

6[-9+2]-2

6[-7]-2

 

Now, multiplication comes before subtraction in the order of operations. So, multiply 6 x -7:

-42-2

 

Simply subtract:

-44

And there you have your final answer!