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SOLUTION
To get the best estimate, let's perform subtraction of the fractions
[tex]\begin{gathered} 14\frac{1}{5}-2\frac{5}{6} \\ \end{gathered}[/tex]First, let us change the mixed fractions to improper fractions, we have
[tex]\begin{gathered} \text{Now, }14\frac{1}{5},\text{ we say 5}\times14\text{ = 70, 71 + 1 = 71,} \\ \text{this becomes } \\ \frac{71}{5} \\ \text{Now, 2}\frac{5}{6},\text{ we say 6}\times2\text{ = 12, 12 + 5 = 17,} \\ \text{this becomes } \\ \frac{17}{6} \end{gathered}[/tex]Subtracting the improper fractions we have
[tex]\begin{gathered} \frac{71}{5}-\frac{17}{6} \\ Now\text{ multiply the denominators} \\ 5\times6=30,\text{ this becomes the least common multiple } \\ \text{place the 30 as the common denominator } \\ \frac{\square}{30} \\ \text{cross multiply and place the result as the numera}tor\text{ } \\ 71\times6=426 \\ 17\times5=85 \\ we\text{ have } \\ \frac{426-85}{30} \\ =\frac{341}{30} \end{gathered}[/tex]Breaking the fraction we have
[tex]\begin{gathered} \frac{341}{30} \\ =11\frac{11}{30} \end{gathered}[/tex]Looking at the options, the closest to this is 11, option B
