In the Name of Allah, The Most Gracious, Most Merciful
Answer:The prophet (PBUH) said:
"Whoever fasts Ramadan, then follows it with six from Shawwal, it will be as if he fasted for a lifetime."
This Noble Hadith includes social, religious, healthy indications. The healthy indication is that the sudden shift from the state of fasting- which requires refraining from eating and drinking to the normal state causes health problems. Therefore, there should be a gradual shift from fasting thirty days to fasting six consecutive or non-consecutive days. The social indication is that perhaps your wife was not able to fast for some days of Ramadan because of a religious excuse (because of her menstrual period for example), so when you fast together the six days of Shawwal, you will not let her fast alone making compensating the missed days of fasting, and so she will be happy with this noble gesture of you. The religious indication is mentioned in the following Noble Hadith Qudsi in which the Prophet, peace be upon him, narrated that Allah the Almighty says:
"And the most beloved thing with which My slave comes nearer to Me, is what I have enjoined upon him; and My slave keeps on coming closer to Me through performing Nawafil (voluntary prayers or doing extra deeds besides what is obligatory) until I love him…"