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Default Count Based on Comparison with Two Fields

I recently learned that I can count the number of items in one column that
match items in another column by using:

=COUNT(MATCH( 'Sheet1'!G2:G15001, 'Sheet2'!A2:A15, 0))

However, I now need to count records on one sheet in which TWO fields match
items in both of two separate columns (i.e., a comparison of two columns to
two columns and a count of records in the first that have fields matching
elements in the second) .

My attempt to use the above statement with an AND failed. Can someone
explain how to do this?
 
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