$$\frac{6}{7}+2\frac{1}{14}+3\frac{2}{21}=$$
$\frac{253}{42}\approx 6.023809524$
$$\frac{6}{7}+\frac{28+1}{14}+\frac{3\times 21+2}{21}$$
$$\frac{6}{7}+\frac{29}{14}+\frac{3\times 21+2}{21}$$
$$\frac{12}{14}+\frac{29}{14}+\frac{3\times 21+2}{21}$$
$$\frac{12+29}{14}+\frac{3\times 21+2}{21}$$
$$\frac{41}{14}+\frac{3\times 21+2}{21}$$
$$\frac{41}{14}+\frac{63+2}{21}$$
$$\frac{41}{14}+\frac{65}{21}$$
$$\frac{123}{42}+\frac{130}{42}$$
$$\frac{123+130}{42}$$
$$\frac{253}{42}$$
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$\frac{11 \cdot 23}{2 \cdot 3 \cdot 7} = 6\frac{1}{42} = 6.023809523809524$