Transition/Transversion ratio
You are almost on the right path.

This schematics from Wikipedia is quite clear in my opinion.





Slightly more chemical explanation (which you do not necessarily need to do bioinformatics, however I think it is always better to know exactly what you are dealing with outside of the computer!)

The idea is that you have four basic nucleotides: cytosine and thymine are called pyrymidines and adenine (A) and guanine (G) which are called purines. Pyrymidines are characterised by a 6 carbon azo-ring which is called a pyridine, while purines have a larger double ring, formed by a pyridine ring + an imidazole ring.

A transition is defined as the passage purine -> purine or pyrimidine -> pyrimidine.
A transversion is the passage purine -> pyrimidine, or viceversa.

These mutations can be caused for instance by certain chemicals, such as alkylating agents, or by ionizing radiations.



In your specific example, given the sequences

 ACGATG 
 TCAGTG


You have 3 mutations:

A -&gt; T  
G -&gt; A
A -&gt; G


So you have 1 transversion (from the purine A to the pyrimidine T) and two transitions (between the purines A and G).