To solve for \( x \) in the equation
\[ x + 16 - 24 \times 68 - 128 + 777 = 78, \]
we first simplify the expression step by step.
Calculate \( 24 \times 68 \): \[ 24 \times 68 = 1632. \]
Substitute this back into the equation: \[ x + 16 - 1632 - 128 + 777 = 78. \]
Now simplify the constants on the left side: \[ 16 - 1632 - 128 + 777. \]
Let's combine these constants: \[ 16 - 1632 = -1616, \] \[ -1616 - 128 = -1744, \] \[ -1744 + 777 = -967. \]
Now our equation looks like this: \[ x - 967 = 78. \]
To isolate \( x \), we can add 967 to both sides: \[ x = 78 + 967, \] \[ x = 1045. \]
So the solution is
\[ \boxed{1045}. \]