To simplify this expression, I need to follow the order of operations: parentheses, exponents, multiplication and division, and addition and subtraction. I can use the acronym PEMDAS to help me remember the order of operations. There are no parentheses or exponents in this expression, so I can skip those steps. Next, I need to look for any multiplication and division operations and do them from left to right. I see that there is a division operation, $10\div2$, and a multiplication operation, $2\cdot3$, in the expression. I can simplify $10\div2$ to $5$, and $2\cdot3$ to $6$. This gives me $4+5-6$. Now, I only have addition and subtraction operations left, so I can do them from left to right. I can simplify $4+5$ to $9$, and $9-6$ to $3$. This is the final simplified value of the expression. 
What is $4+10\div2-2\cdot3$?