He had intercourse with his wife when she was observing a voluntary fast
Question

                What is the ruling on one who has intercourse with his wife when she is fasting the six days of Shawwal and he is not fasting?.
Praise be to Allah.The one who is observing a 
    voluntary fast has the choice: he may complete the fast or he may break it, 
    but completing it is better. 
Ahmad (26535) narrated from 
    Umm Hani (may Allah be pleased with her) that the Messenger of Allah 
     (peace and blessings of Allah be upon him) entered upon her. He called 
    for a drink and drank some, then he passed it to her and she drank some. She 
    said: O Messenger of Allah, I was fasting. The Messenger of Allah  
    (peace and blessings of Allah be upon him) said: “The one who is observing 
    a voluntary fast has the choice; if he wishes he may fast and if he wishes 
    he may break the fast.” Classed as saheeh by al-Albani in Saheeh 
    al-Jami’ (3854). 
Please see also the answer to 
    question no. 49610. 
If a person fasts one of 
    the six days of Shawwal, and he wants to break the fast, he may do so, 
    whether he does it by eating, having intercourse, or anything else. 
If this woman fasted 
    without her husband’s permission, then he may call her to his bed, and she 
    has to respond. 
But if she was fasting with 
    his permission, then he does not have the right to spoil her fast, but if he 
    wants that then it is better for her to respond to him. 
Ash-Shaykh Ibn ‘Uthaymeen (may 
    Allah have mercy on him) said: If she observes a nafil fast with his 
    permission, then it is not permissible for him to spoil her fast, because he 
    gave her permission. But in that case if she is observing a nafil fast with 
    his permission and he wants her to come to his bed, is it better for her to 
    continue fasting and refuse her husband’s request? The other option is 
    better, which is responding to her husband’s request, because responding to 
    her husband’s request is basically obligatory, and the voluntary fast is 
    mustahabb, and because if she refuses even though his desire is strong, then 
    he may feel some resentment towards her and the relationship between them 
    may be affected as a result of that. 
Majmoo’ Fatawa Ibn 
    ‘Uthaymeen (21/174). 
And Allah knows best.