I think your lenghts are backwards. From the picture l1 < l2, but in the problem it says l1 > l2. I will go by the picture.
Sum of the moments about the pivot point = I*alpha
Find the moment of inertia:
Treat the blocks as point masses.
I_point mass = m*r^2
I_LHS = m*l1^2
I_RHS = m*l2^2
I_total = I_RHS + I_LHS = m*l1^2 + m*l2^2 = m*(l1^2 + l2^2)
What are the moments? Moments that produce CCW spin will be treated as positive. The mass on the left hand side produces a moment of m*g*l1, which makes the system want to spin CCW (positive). The mass on the right hand side produces a moment of m*g*l2, hich makes the system want to spin CW (negative).
Sum of the moments (CCW = +) = m*g*l1 - m*g*l2 = I_total*alpha
m*g*l1 - m*g*l2 = I_total*alpha
alpha = (m*g*l1 - m*g*l2) / I_total = m*g*(l1 - l2) / (m*(l1^2+l2^2)) = g (l1-l2) / (l1+l2)^2
Plug in numbers, remember to convert cm to m:
alpha = -5.13 rad/s^2
The negative means that the system is going to rotate in the clockwise direction. This means that the LHS is rising.
The tangential/agular acceleration relatonship
a = alpha*r
The radius in this case is l1
a = alpha*l1
Sub in alpha, but since we know it is going up, treat alpha as a positive number so our acceleration will be positive (up).
a = 5.13 rad/s^2 * 0.13 m = 0.667 m/s^2 <--- ANS
Hope I helped explain it.