Something's wrong with the problem or else I am interpreting 
it wrong.  

1. Suppose the 2-digit number were very large, say 99, the 
largest 2-digit number. then if you added a 2 on each end,
you'd have 2992, but the product of the digits would be only
2*9*9*2 = 324, but 2222 times the original number 99 is 219978, 
much larger than 324.

2. Suppose the 2-digit number were very small,
say 11, a small 2-digit number.  Then if you added a 2 on each 
end, you'd have 2112, but the product of the digits would be 
only 2*1*1*2 = 4, but 2222 times the original number 11 is 
24442, much larger than 4.

With this interpretation, there can be no solution.  If I am 
interpreting it incorrectly, then you may tell me the correct 
way to interpret it in the thank-you note form below and I'll 
get back to you by email.

Edwin