we know that
case 1) The price of a dozen eggs was [tex]\$1.63[/tex]
In this moment the original price of a dozen eggs is [tex]\$1.63[/tex]
case 2) The price rose [tex]\$m[/tex]
In this moment the new price of a dozen eggs is [tex]\$1.63+\$m[/tex]
case 3) The price dropped [tex]\$0.12[/tex] per dozen
The final price of a dozen eggs is
[tex]\$1.63+\$m-\$0.12[/tex]------>[tex]\$1.51+\$m[/tex]
therefore
the answer is
[tex]m+1.51[/tex]