I have a slight trouble with understanding the concept of calculation the standard error of the mean from combined averages.

Let's say he have following data points:

a = 10.19

b = 10.59

c = 10.43

average_a = 10.40 and st.err._a = 0.12

And a second set:

d = 10.69

e = 10.34

f = 10.29

average_b = 10.44 and st.err._b =0.12

I am interested in the difference between the sample sets:

average_b - average_a = 0.04

How do you approach calculating the standard error of the mean now?

Thanks,

Salfina