Step 1: Note the starting frequency.
The light begins at $\nu = 2\nu_0$, which is above the threshold $\nu_0$, so electrons come out at first.
Step 2: Find the new frequency.
The frequency is cut to one third: $\nu' = \tfrac13(2\nu_0) = \tfrac{2}{3}\nu_0$.
Step 3: Compare with threshold.
Now $\tfrac{2}{3}\nu_0$ is less than $\nu_0$, so the light no longer has enough energy per photon to free any electron.
Step 4: Effect of intensity.
Doubling intensity only adds more photons, but each is still too weak, so no current flows.
\[ \boxed{\text{The current will be zero}} \]