



 
HI Malik, I would do it in two steps. First convert the number you have in base 6 to base 10, and then convert the base 10 expression to base 4. For example let's look at $1023_6$ which is read five three one base 6. To express this number in base 10 think of what $1023_6$ means. \[1023_6 = 1 \times 6^3 + 0 \times 6^3 + 2 \times 6 + 3 = 1\times 216 + 0 \times 36 + 2 \times 6 + 3 = 216+ 12 + 3 =231.\] Thus $1023_6 = 231_{10} = 231.$ To express 231 in base 4 you repeatedly divide by 4 and record the remainders. Here is the table I used to keep track.
Reading the remainders from the bottom to the top I see 3213. Thus 231 is $3213_{4}.$ Hence $1023_6 = 3213_{4}.$ If this is not clear think of it this way. Suppose you have 231 marbles and some paper bags. Arrange the marbles by putting 4 in each bag and you have 57 bags of 4 marbles each and 3 remaining marbles. You also have some cardboard boxes, each box large enough to hold 4 bags of marbles. Arranging them this way you have 14 boxes with 4 bags each and 1 bag remaining. Now arrange the boxes into stacks of 4 boxes each and you have 3 stacks with 2 boxes remaining. Hence you have 3 stacks, 2 boxes, 1 bag and 3 marbles which is $3 \times 4^3 + 2 \times 4^2 + 1 \times 4 + 3$ marbles $=3213_4$ marbles. I hope this helps,  


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