How to calculate the standard error of the mean after subtracting averages

#1
Hi!
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