When attempting larger mental multiplications, there is a tendency for many people to try and replicate the long-hand method used when multiplying on paper. This tends to work from right to left, dealing essentially with the detailed end of the solution before the bigger-picture end. Such paper-based methods do this in order to identify digits that need to be carried over to columns on their left.
This approach, however, presents certain problems in the context of mental multiplication, as there are great practical benefits to be derived from arriving quickly at a big-picture approximation and filling in detail towards the end. Also, our memories are typically not good at working on one problem while trying to remember digits that are due to be carried over.
Also, be aware of why many people consider the times table to be limited to 12 x 12 when, in this decimal era the number 12 seems a rather strange limit. But this goes back to the days of counting in dozens (e.g. 12 inches in a foot) when an English shilling was worth 12 pennies.