What does it mean that multiplication and division have the same precedence?

When there is equal precedence, the standard thing to do is to work from left to right. Hence $$80/10\times 2 = (80/10)\times2=16. $$

It should be noted that this is not completely universal, i.e. some programming languages don't do it this way, as far as I know. Anyway, it doesn't really matter that much because no one actually writes $80/10\times2$, instead they write $(80/10)\times2$ to remove any ambiguity.

I'm fine with Eff's answer because I don't think my question was particularly clear. But I'd like to offer what I hope is a clearer question and answer.

When learning about order of operations, examples of mathematical ambiguity like the following often come up:

What is $2 + 4 \times 6$?

The teacher then demonstrates to the pupil that by performing this computation in a different order of operations, we get two different answers. So we use order of operations to indicate that the real answer is $2 + (4 \times 6) = 26$, not $(2 + 4) \times 6 = 36$. In other words, order of operations removes the ambiguity of which operation to perform first.

When I heard that two operations have "equal" precedence, my interpretation of that was that it does not matter which order you perform your operations. But mathematically, this cannot be true since:

$$ (80 \div 10) \times 2 \neq 80 \div (10 \times2) $$

While $\div$ and $\times$ have equal precedence.

Clearly, something else is meant by "equal". Implicit in Eff's answer is that by "equal" we mean that the ambiguity cannot be resolved by simple precedence. The ambiguity is resolved by a new left-to-right rule.

To answer my own question, "What does it mean that multiplication and division have the same precedence?" I say: it means that you cannot perform multiplication or division first as a rule and in fact you will get different answers depending on context. The real rule is that you perform operators with equal precedence in a left-to-right computation.