4 , 7 : 1 , 3 = x : 2 , 6

To solve the proportion \( \frac{4}{7} : \frac{1}{3} = \frac{x}{2.6} \), we first interpret the colons as fractions, giving us:

\[ \frac{4/7}{1/3} = \frac{x}{2.6} \]

Now, simplify the left side:

\[ \frac{4/7}{1/3} = \frac{4}{7} \times \frac{3}{1} = \frac{4 \times 3}{7 \times 1} = \frac{12}{7} \]

Now we have the equation:

\[ \frac{12}{7} = \frac{x}{2.6} \]

Next, we cross-multiply to solve for \( x \):

\[ 12 \times 2.6 = 7 \times x \]

Calculating \( 12 \times 2.6 \):

\[ 12 \times 2.6 = 31.2 \]

So now we have:

\[ 31.2 = 7x \]

Now, divide both sides by 7 to find \( x \):

\[ x = \frac{31.2}{7} = 4.45714285714 \approx 4.46 \]

Thus, the value of \( x \) is approximately 4.46.