\[\boxed{\text{6.262.}}\]
\[\textbf{а)}\ 31 \cdot (m + 378) = 17\ 267\]
\[m + 378 = 17\ 267\ :31\]
\[m + 378 = 557\]
\[m = 557 - 378\]
\[m = 179.\ \]
\[Ответ:179.\ \]
\[\textbf{б)}\ 202 \cdot (192 + n) = 98\ 980\ \]
\[192 + n = 98\ 980\ :202\]
\[192 + n = 490\]
\[n = 490 - 192\]
\[n = 298.\ \]
\[Ответ:298.\ \]
\[\textbf{в)}\ 43\ 966\ :(z - 105) = 1\ 157\]
\[z - 105 = 43\ 966\ :1\ 157\]
\[z - 105 = 38\]
\[z = 38 + 105\]
\[z = 143.\ \]
\[Ответ:143.\ \]
\[\textbf{г)}\ 27\ 384\ :(3\ 912 - x) = 7\]
\[3\ 912 - x = 27\ 384\ :7\]
\[3\ 912 - x = 3\ 912\]
\[x = 3\ 912 - 3\ 912\]
\[x = 0.\ \]
\[Ответ:0.\]