Fully simplify $$ 4 x y+3 x+6+2 y x+x+y $$

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To fully simplify the expression $$ 4xy + 3x + 6 + 2yx + x + y $$, follow these steps:

1. **Combine Like Terms:**
   - **Terms involving $$ xy $$:** 
     $$
     4xy + 2yx = 4xy + 2xy = 6xy
     $$
   - **Terms involving $$ x $$:**
     $$
     3x + x = 4x
     $$
   - **Constant and $$ y $$ terms:**
     $$
     6 + y
     $$

2. **Rewrite the Simplified Expression:**
   $$
   6xy + 4x + y + 6
   $$

There are no further like terms to combine, and the expression cannot be factored further with integer coefficients.

**Final Simplified Form:**
$$
6xy + 4x + y + 6
$$

**Answer:**  
After simplifying, the expression is 6 x y + 4 x + y + 6.
The simplified expression is $$ 6xy + 4x + y + 6 $$.

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