Differences in Postfix Syntax
There are no "rules", you make the rules yourself. The rule used in class has the property that the numbers appear in the same order in both expressions. The rule is also pretty natural:

$$ T(\alpha \circ \beta) = T(\alpha) T(\beta) \circ $$

Here $\alpha$ is an infix expression, $T(\alpha)$ is the translation of $\alpha$, and $\circ$ is a binary operation. The corresponding rule for unary expressions is $T(\circ \alpha) = T(\alpha) \circ$, and there is also a deparenthesizing rule, $T((\alpha)) = T(\alpha)$. If you apply these rules to the expression $4 + (5 * 6)$ you will get $4 \; 5 \; 6 * + $.

Keeping the order is important for operations which are not commutative, such as subtraction and division; that's assuming on the convention that $3 \; 2 \; - = 1$ and so on, rather than the other way around.