To solve these problems, we need to convert all mixed numbers to improper fractions.

1) 3 1/3 + 5/6
To convert 3 1/3 to an improper fraction, we multiply the whole number (3) by the denominator (3) and add the numerator (1). This gives us (3*3 + 1) / 3 = 10/3.
Now we can add the fractions: 10/3 + 5/6.
To add fractions, we need to find a common denominator, which in this case is 6.
We multiply the numerator and denominator of the first fraction by 2 to get 20/6.
Now we can add the fractions: 20/6 + 5/6 = 25/6.
The answer is 25/6.

2) 4 5/7 - 2 11/21
To convert 4 5/7 to an improper fraction, we multiply the whole number (4) by the denominator (7) and add the numerator (5). This gives us (4*7 + 5) / 7 = 33/7.
To convert 2 11/21 to an improper fraction, we multiply the whole number (2) by the denominator (21) and add the numerator (11). This gives us (2*21 + 11) / 21 = 53/21.
Now we can subtract the fractions: 33/7 - 53/21.
To subtract fractions, we need to find a common denominator, which in this case is 21.
We multiply the numerator and denominator of the first fraction by 3 to get 99/21.
Now we can subtract the fractions: 99/21 - 53/21 = 46/21.
The answer is 46/21.

3) 3 1/4 x 2/5
To convert 3 1/4 to an improper fraction, we multiply the whole number (3) by the denominator (4) and add the numerator (1). This gives us (3*4 + 1) / 4 = 13/4.
Now we can multiply the fractions: 13/4 x 2/5.
To multiply fractions, we multiply the numerators together and the denominators together: (13*2) / (4*5) = 26/20.
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2: 26/20 = 13/10.
The answer is 13/10.

4) 4 7/8 : 1/4
To convert 4 7/8 to an improper fraction, we multiply the whole number (4) by the denominator (8) and add the numerator (7). This gives us (4*8 + 7) / 8 = 39/8.
Now we can divide the fractions: 39/8 : 1/4.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: 39/8 x 4/1 = 39/2.
The answer is 39/2.