To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, we need to simplify the fractions within the expression.

6/7.8/13 = (6/7) * (8/13) = 48/91

Next, we can rewrite the expression with the simplified fraction:

48/91 + 6/7.9/13.3/13.6/7

Now, let's simplify the remaining fractions:

6/7.9/13.3/13.6/7 = (6/7) * (9/13) * (3/13) * (6/7) = 1944/2541

Finally, we can rewrite the expression with the simplified fraction:

48/91 + 1944/2541

To add these fractions, we need to find a common denominator:

The prime factorization of 91 is 7 * 13, and the prime factorization of 2541 is 3 * 13 * 17.

The common denominator is 7 * 13 * 3 * 17 = 4281.

Now, we can rewrite the fractions with the common denominator:

48/91 + 1944/2541 = (48 * 47)/(91 * 47) + (1944 * 17)/(2541 * 17)

= 2256/4281 + 33048/4281

= (2256 + 33048)/4281

= 35304/4281

= 8.247

Therefore, the simplified value of the expression is approximately 8.247.