Charles Spurgeon and his wife, according to a story in the Chaplain magazine, would sell, but refused to give away, the eggs their chickens laid. Even close relatives were told, “You may have them if you pay for them.” As a result some people labeled the Spurgeons greedy and grasping.
They accepted the criticisms without defending themselves, and only after Mrs. Spurgeon died was the full story revealed. All the profits from the sale of eggs went to support two elderly widows. Because the Spurgeons where unwilling to let their left hand know what the right hand was doing (Matthew 6:3), they endured the attacks in silence.
Jesus said in Matt. 6:3, “But when you give to the needy, do not let your left hand know what your right hand is doing.” For a long time, I’ve been reading this verse. I could not understand it. How can the left hand not know what the right hand is doing? Both are attached to the same brain! But I’ve done some research about it. I’d like to share the explanation with you.
The right way of giving to the poor is by the right hand. The left hand should not know what the right hand is doing. For the left hand NOT to know what the right hand is doing, it means that the right hand is doing it secretly. It means that the right hand is giving confidentially. It means the right hand is giving covertly. The giving of the right hand is so secret and confidential that the left hand does not know what the right hand is doing.
This does not mean that we will not keep a record of givers. It does not mean that we will not practice good accounting. It does not mean that we will not practice financial transparency. It simply means that we will not give out of selfish motives, to gain people’s praises. (Blomberg)
In the context of v. 2, the left hand does not know what the right hand is doing because the right hand is not blowing trumpets. The right hand is not giving to the poor in front of people to see. The right hand is not giving to get the praise of people. Rather, the right hand is giving without any secret, selfish motive. Because the right hand has no selfish motives, the left hand does not notice it.
 “Giving.” Cited August 16, 2014. Online: http://www.sermonillustrations.com/a-z/g/giving.htm