To multiply 47293851 by 68027419 exactly, we can use the standard long multiplication method.

Let $A = 47293851$ and $B = 68027419$.

We will multiply $A$ by each digit of $B$ from right to left, and then sum the results.

$A \times 9 = 47293851 \times 9 = 425644659$
$A \times 10 = 47293851 \times 1 = 47293851$ (shifted by one position)
$A \times 400 = 47293851 \times 4 = 189175404$ (shifted by two positions)
$A \times 7000 = 47293851 \times 7 = 331056957$ (shifted by three positions)
$A \times 20000 = 47293851 \times 2 = 94587702$ (shifted by four positions)
$A \times 000000 = 47293851 \times 0 = 0$ (shifted by five positions)
$A \times 8000000 = 47293851 \times 8 = 378350808$ (shifted by six positions)
$A \times 60000000 = 47293851 \times 6 = 283763106$ (shifted by seven positions)

Now we align and sum these products:

```
        47293851
      x 68027419
      -----------
       425644659   (47293851 * 9)
      47293851     (47293851 * 1, shifted 1 position)
     189175404     (47293851 * 4, shifted 2 positions)
    331056957      (47293851 * 7, shifted 3 positions)
   94587702        (47293851 * 2, shifted 4 positions)
  00000000         (47293851 * 0, shifted 5 positions)
 378350808         (47293851 * 8, shifted 6 positions)
283763106          (47293851 * 6, shifted 7 positions)
-------------------
3217277636181769
```

Let's perform the addition carefully:

```
          425644659
        +  472938510
        +   8917540400
        +  31056957000
        + 458770200000
        +          0
        +37835080800000
        +283763106000000
---------------------------
3217277636181769
```

Let's re-do the multiplication and addition step by step to ensure accuracy.

```
       47293851
    x  68027419
    --------------
      425644659   (47293851 * 9)
     47293851     (47293851 * 10)
    189175404     (47293851 * 400)
   331056957      (47293851 * 7000)
  94587702        (47293851 * 20000)
 00000000         (47293851 * 000000)
378350808         (47293851 * 8000000)
283763106         (47293851 * 60000000)
------------------------------
283763106000000
  37835080800000
     945877020000
      331056957000
        18917540400
          472938510
            425644659
------------------------------
3217277636181769
```

Final verification:
$47293851 \times 68027419 = 3217277636181769$

The final answer is $\boxed{3217277636181769}$.
