Can I crack an AES string if I have all these parameters? This is for a challenge at followthewhiterabbit.trustpilot.com: 


  Knowns:
  
  
  The algorithm is AES (Rijndael)
  Blocksize: 128
  Keysize: 256
  You only need to find the first 6 bytes of the key, the rest are 0’s, so:
  [?,?,?,?,?,?,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
  All bytes in the key has an integer value between 0 and 16.
  The initialization vector is (base64 encoded): "DkBbcmQo1QH+ed1wTyBynA=="
  The text is just plain ASCII english
  
  
  The encrypted text (base64 encoded):
  
  [base 64 block follows]


Can I crack an AES string if I have all these parameters? If so, how should I do it?
Since there are only $16^6 \approx 16.8$ million keys, you can try them all and decrypt the message with each. In general you would have to know something about the plaintext to identify which of those decrypted candidates is the correct one.

In this case it is known that the message is English ASCII, so the top bit of each plaintext byte will be 0. The chance of an $n$-byte message succeeding that test by chance is $2^{-n}$, so with more than 24 bytes of data (as you have) it is likely you will find a unique key that decrypts it into ASCII. The padding could include a 1 bit, so you might want to ignore the last block until you've found the key.

Remember to try different modes of operation if the first doesn't work – there is an IV, so it isn't ECB. If the ciphertext length was not a multiple of the block size, it would likely be CTR mode, but yours is.