How should I approach her and apologise?

I have had a lot of worries lately, one of my family members has been ill and I have been extremely worried about them. The knock on effect of this is that my mood of late hasn't been the best, A woman who I know likes me has become angry with me because I probably haven't shown her a lot of attention lately.

I feel awful about this and realise it could be too late to repair, but how do I approach her to genuinely say I'm sorry

How should I approach her and apologise?
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