Mr. Smythe places 10,000 in a savings account that earns 6

Curly, try and solve the problem - its pretty simple.

I get the total amount at the end of the second year as 10600 in first account and 660 in second account = total of 11260

Mr. Smythe places 10,000 in a savings account that earns 6 percent simple annual interest. At the end of the year, he withdraws the interest that has accumulated during the year, and places it in a seperate account that earns 10 percent simple annual interest. What is in the account(s) at the end of the second year?
(1) How can there be any in the first account if he withdraws it from the first?
(2) the problem says nowhere to add back the 10,000.

there's NOTHING questionable here: simple and clear as 1+1=2

your question (1): he withdraws the interest ONLY
your question (2): the 10,000 STAYS in first account

Year#1:
10000 * .06 = 600 = interest during the year

Year#2:
10000 * .06 = 600 + 10000 = 10600 : amount in 1st account
600 * .10 = 60 + 600 = 660 : amount in 2nd account

If he withdraws the interest he earned during the first year, how can it stay in the first account, i.e.- 10,600?

This is Kap's problem; I doubt it ETS words it in this style.
VT

curly - the problem is perfectly worded - you just missed "the catch". Yes, the $600 was taken out of the account at the end of year 1. HOWEVER, the account with $10K earns an ADDITIONAL $600 in the 2nd year - the question asks how much money is in the accounts at the end of 2 years.