Given:

• First term \( \rm a_1 = 12 \)
• Common difference \( \rm d = -3 \)

We can use the formula for the sum of the first \( \rm n \) terms of an arithmetic series:

\[ \rm S_n = \frac{n}{2}(2a_1 + (n - 1)d) \]

Substitute the given values:

\[ \rm S_{32} = \frac{32}{2}(2 \times 12 + (32 - 1) \times (-3)) \]

\[ \rm S_{32} = 16(24 + 31 \times (-3)) \]

\[ \rm S_{32} = 16(24 - 93) \]

\[ \rm S_{32} = 16 \times (-69) \]

\[ \rm S_{32} = -1104 \]

So, the sum of the series \(12 + 9 + 6 + \ldots\) up to 32 terms is \(-1104\).