6. (10 points) Color 6 squares of a $4 \times 4$ grid with the same color. If a column has colored squares, they must be colored from the bottom square upwards. In adjacent columns, the number of colored squares in the left column must be greater than or equal to the number of colored squares in the right column (as shown in the figure). There are $\qquad$ ways to color the grid.
【Analysis】According to the requirements, 6 squares in a $4 \times 4$ grid are to be colored, with the number of colored squares on the left side being greater than or equal to the number on the right side. Break down 6 into the sum of several numbers, with the largest number on the left being 4, for example, $4+1+1=6$, coloring starting from the first column or from the second column results in 2 patterns;
$4+2=6$, coloring starting from columns $1$, $2$, or $3$ results in 3 patterns;
$3+2+1$, coloring starting from columns $1$ or $2$ results in 2 patterns;
$3+1+1+1$, coloring starting only from the first column results in 1 pattern;
Adding them up, we get the solution.
【Solution】Solution: As shown in the figure, $2+3+2+1=8$ (patterns),

Answer: There are a total of 8 patterns for coloring.
Therefore, the answer is: 8.