I'm slightly dubious that you solved A). and B). on your own but you're having trouble with C).
In order to save myself a lot of work, I'll take your word for it. The answers shown there for A). and B). are correct, so I'll go directly to C).
The block breaks free of static friction and starts moving when there are 86 washers in the bucket.
Total mass of the bucket and washers is (0.120 kg) + 86(0.02 kg) = 1.84 kg
Total weight of the bucket & washers = (M) (G) = (1.84 x 9.8) = 18.04 N
That's the tension in the string, sliding the block along the table towards the edge.
How much force of friction is pulling the block back, not letting it move ?
It's (weight of the block) x (coefficient of kinetic friction)
(M) (G) x (0.34) = (4.4) x (9.8) x (0.34) = 14.66 N
The block has 18.04 N pulling it forward, and 14.66 N holding it back.
What's the net force on the block ?
18.04 - 14.66 = 3.38 N forward, toward the pulley.
Take the magic formula that always connects acceleration with net force:
F = M A
You know 'F' and 'M' and you need to find 'A', so Divide each side by (M):
A = F / M and there you have it for the block.
A= F / M = (3.38 N) / (4.4 kg) = 0.768 meter / second-squared
