When you take the approach of developing mental multiplication skill to address the need for solving problems listed in the times table, it is really helpful to develop a strategy of identifying the fastest (normally the easiest) route to solving any particular multiplication problem. By doing this at outset, the steps required to arrive at the final answer to the multiplication problem are much easier to handle, and can often be run through at a speed similar to that with which rote-learning students are able to recall the answers from memory.
With practice, the speed difference can be so negligible that any observer may think that you are recalling answers from memory, and certainly with greater confidence in the accuracy of answers.
In recent years, many people have challenged how appropriate it is to attempt to learn the times table up to 12x12. Some prefer to limit the learning objective to 10x10 often citing decimalization as the reason for this, without speaking out the truth which underlies their motivation, being a preference to dumb-down the learning objective as it is then easier to accomplish.
On the other hand, those who value the ability to multiply (typically those who are comfortable themselves and often fail to see the problem through other people's eyes) suggest raising the bar to empower students with skills based on enlarging the times table to cover up to 20x20 or even 100x100. This kind of goal cries out for a skill-based approach, rather than memorization of number facts.