You can treat the criteria on multi-valued properties just like other criteria. For example, the following query will find all nodes that have a value of 'white dog' on the 'someProp' property:
SELECT * FROM [nt:unstructured] WHERE someProp = 'white dog'
If the 'someProp' property has multiple values, then a node with at least one value that satisfies the criteria will be included in the results.
To find nodes that have multiple values of a multi-valued property, simply AND together multiple criteria. For example, the following query will return all nodes that have both of the specified values:
SELECT * FROM [nt:unstructured] WHERE someProp = 'white dog'
AND someProp = 'black dog'
Any of the operators will work, including 'LIKE':
SELECT * FROM [nt:unstructured] WHERE someProp LIKE '%white%'
AND someProp LIKE '%black%'
Other combinations are possible, of course.