To solve the expression \(0.46 \times 7.8 + 2.2 \times 15.6\), let's calculate each term step by step.

1. **Calculate \(0.46 \times 7.8\):**
\[
0.46 \times 7.8 = 3.588
\]

2. **Calculate \(2.2 \times 15.6\):**
\[
2.2 \times 15.6 = 34.32
\]

3. **Now, add the two results together:**
\[
3.588 + 34.32 = 37.908
\]

So, the final result is:
\[
\boxed{37.908}
\]