Your mother should also have the TSH repeated to confirm.
The free t3 and free t3 are the recommended tests as AR-10 said.
A TSH of 12.4 indicates she is hypothyroid. The TSH should be between 1.0 and 2.0, roughly.
The Total T4 test and the Total T3 tests do not provide very specific information as they are not acurate tests. A Free T4 and a Free T3 are better tests.
It is also hard to comment on the T4/T3 tests without knowing the tests ranges used by the particular lab.
The TSH test strongly suggests she should be put on thyroid medication, but without a Free T4 test to compare it to, that is only a guess.