Interested in Language
This exercise is written in my book;
E. Complete the sentences.
Situation 2: You and a friend are spending your first day visiting Athens.
3. Do you think we might get better directions if we .......... (know) how to speak Greek? (Answer key=Knew)
Why not "Know"? As you know, "might" can be used in both conditional I and Conditional II. Then it's really difficult to recognize whether "might" refers to which one.
I have taken a picture of the page.
If you click here, you will see it.
Source: Summit 2B (by Joan Saslo and Allen Ascher) Pearson
Longman Press, Unit6, Conditionals.
'Know' would just about be possible if you were talking about a future situation, and perhaps suggesting to your friend that you learnt some Greek to avoid difficulties. However, the instructions tell you that you are in a present-time situation. Therefore the only thing that makes sense is your not knowing Greek. 'If we knew ...' is therefore the correct tense for a hypothetical/counterfactual (second conditional) sentence.