To have removed at most 2 pennies out of 4 coins, you could have either selected 4 nickels, 3 nickels and 1 penny, or 2 nickels and 2 pennies.
There is only one way to select 4 nickels: 6/11 x 5/10 x 4/9 x 3/8 = 1/22
There are four ways to select 3 nickels and 1 penny; each way is: 6/11 x 5/10 x 4/9 x 5/8 = 1/66
4 x 1/66 = 2/33
There are six ways to select 2 nickels and 2 pennies; each way is: 6/11 x 5/10 x 5/9 x 4/8 = 5/66
6 x 5/66 = 5/11
Adding these probabilities: 1/22 + 2/33 + 5/11 = 37/66