Help me, I am new to discrete math

I was lost in the first day of class. He listed all the axiom from 1 to 13. Then he start proving things. For example:

Theorm

For all real number X

The additive inverse -X is unique.

Proof

Let Y and Z be additive inverse of X.

Y = Y + 0....................( axion 5, additive identity )

Y = Y + ( X + Z )..........( Z is additive inverse of X )

Y = (Y + X ) + Z...........( axion 3, associative law )

Y = 0 + Z.....................( Y is additive inverse of X )

Y = Z .........................( 0 is additive identity )

The prove above. I understand perfectly.

Here are some of the things that I need to prove but I don't know how to prove. Please teach/tell me how to do the following questions.

Question 3:

Prove that ( -X * Y ) is equal to ( X * -Y )

Question 6:

if X + Z = Y + Z prove that X equal to Y

Questions are from [link removed]

If you teach me how to do that those 2 question, I think i know how to do the rest hopefully.

Edited: To clarify, I was in a rush before