To find the ratio of the number of empty tables to the total number of tables at Javier's Italian Restaurant, we start by determining the number of empty tables.
The total number of tables is 26, and if 6 of those tables are full, we can calculate the number of empty tables as follows:
\[ \text{Number of empty tables} = \text{Total tables} - \text{Full tables} = 26 - 6 = 20 \]
Next, we need to establish the ratio of empty tables to total tables. The ratio is given by the formula:
\[ \text{Ratio of empty tables to total tables} = \frac{\text{Number of empty tables}}{\text{Total number of tables}} = \frac{20}{26} \]
To simplify this ratio, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:
\[ \frac{20 \div 2}{26 \div 2} = \frac{10}{13} \]
Thus, the ratio of the number of empty tables to the total number of tables is
\[ \boxed{\frac{10}{13}}. \]