He would have to look a 26^{4} combinations.

This is because:

2 letter words =

AA to ZZ

AA to AZ is 26 combinations, then you repeat with BA to BZ, CA to CZ etc.

As you repeat this 26 combo thingamajig 26 times,

This means that there are 26^{2} combinations for two letter words.

3 letter words =

AAA to ZZZ

AAA to AAZ is 26 combinations, AAA to AAZ is 26 combinations.

then you repeat with ABA to ABZ, etc.

This means that there are 26^{3} combinations for three letter words.

Therefore..

4 letter words =

AAAA to ZZZZ

AAAA to AAAZ is 26 combinations, then you repeat with AABA to AABZ, AACA to AACZ etc.

This means that there are 26^{4} combinations for four letter words.

Not sure about the answer though...