Hi there, that's because the hb1ac is an average of your levels over 3 months. When you prick your finger it is only giving your level at THAT time, you would not know what your level was in between finger pricking, ie every minute of every day. For example, a person could be recording finger prick tests of 4 every time they checked but between meals or whilst fasting it could be up at 10. The average of that would be 7 and that's what the hb1ac would show. Your averages of around 6 seem to equate to the 39.
Like a finger prick test, HbA1c measurement is not always exact. Studies comparing the results of continuous blood glucose monitoring with HbA1c have shown that the HbA1c can be off by as much as 7 mmol (0.5% in DCCT format) in either direction for a significant number of people (https://academic.oup.com/edrv/article/40/4/988/5487357). One reason for this is that the average survival time of red blood cells is assumed to be the same for all people (which it is clearly not) -- for example, it can be shown for example that with higher blood sugar levels, red cells are much shorter lived than at normal blood sugar levels. This having been said, HbA1c within a person tends to be much more stable than between people with the same average blood sugar levels.