To evaluate the expression \( 10 - 7.8w \) for \( w = 1.2 \), we can substitute \( w \) with \( 1.2 \):
\[ 10 - 7.8(1.2) \]
Now, calculate \( 7.8 \times 1.2 \):
\[ 7.8 \times 1.2 = 9.36 \]
Now substitute this value back into the expression:
\[ 10 - 9.36 \]
Now perform the subtraction:
\[ 10 - 9.36 = 0.64 \]
So, the final answer is:
\[ \boxed{0.64} \]