Answer
The block on the left exerts a force of $\frac{F}{3}$ on the block to its right and this force is directed to the right.
Work Step by Step
We can find the acceleration of the system of both blocks:
$F = (m+2m)~a$
$a = \frac{F}{3m}$
We can find the force $F_p$ with which the block on the right pushes the block on the left:
$F_p = ma = m~(\frac{F}{3m}) = \frac{F}{3}$
By Newton's third law, the block on the left exerts a force of the same magnitude on the block to its right.
The block on the left exerts a force of $\frac{F}{3}$ on the block to its right and this force is directed to the right.
