past simple or present perfect
She has lived in seven different countries this year, so she knows a lot about different cultures. or
She lived in seven different countries this year, so she knows a lot about different cultures.
"She has lived..." is correct. "This year" means from the beginning of the year, up to today's date, so the only answer is present perfect.
Also, the next part of the sentence uses present simple. The timeframe stays consistent.
April 14, 2016
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And just to add something to Peachey's answer:
Remember that the present perfect always tells us something about the present time. In this case, you're giving an explanation about why she now knows a lot about different cultures. Her experience of having lived in these places has an effect on the present situation - hence the present perfect tense.
April 14, 2016
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