SOLUTION: I am a four-digit number. my units digit is twice my thousands digit. my My tens digit is three times my hundreds digit. My units digit is also seven less than my tens digit but

 
I am the number _ _ _ _

So my tens digit is a multiple of 3

So my tens digit is a multiple of 3 large enough to subtract 7 from.
Therefore my tens digit is 9.  So 
I am the number _ _ 9 _


>>My units digit is also seven less than my tens digit<<

Therefore my units digit is 9-7 or 2.  So 
I am the number _ _ 9 2


>>My tens digit is three times my hundreds digit.<<

Therefore my hundreds digit is 3.   
I am the number _ 3 9 2


>>my units digit is twice my thousands digit.<<

So my thousands digit is 1.            
I am the number 1 3 9 2


>>My units digit is...only one less than my hundreds digit<<

We don't need that information, but it checks 
since 2 is 1 less than 3.
I am the number 1392.

Edwin