This is bar 3 of an arrangement of Clair de Lune in 9/8. What is the meaning of the 2 above the beam? The first C is played on beat 4, so the 4 remaining notes in the bar need to cover 6 beats. Which beat is the E played on? What is the total duration of the tied E notes? Is the second C played on beat 9? Listening to recordings hasn't been much help due to amount of rubato used.
These are called duplets. They tell you to play two quavers (8th notes) in the time of three quavers. These are used in compound time-signatures (6/8, 9/8, 12/8, 6/4, 9/4 etc.) where each beat consists of three sub-beats (or sub-divisions). As these time-signatures group notes in threes, a duplet allows you to have two equal length notes in the time of this group of three. Strictly speaking, duplets aren’t necessary in the same way triplets are, as you can instead write the same rhythm using dotted notes. For instance, two dotted quavers equally divide the time taken by three quavers in just the same way a duplet does.