Question 1207871
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k = 3 groups
N = n1+n2+n3 = 6+7+8 = 21


df = degrees of freedom
df1 = k-1 = 3-1 = 2
df2 = N-k = 21-3 = 18


You mention using an F-table, but didn't provide the actual table. 
I'll assume it looks like something found at this link
http://socr.ucla.edu/Applets.dir/F_Table.html


I'll be using the table that has the title "alpha = 0.025" at the top of the table.
Highlight the column labeled df1 = 2 at the top
Highlight the row labeled df2 = 18 at the left side
This row and column intersect to yield the approximate value 4.5597 which rounds to <font color=red>4.56</font>
Therefore the answer is <font color=red>option B</font>


Caution: The order of df1 and df2 is important. Swapping them will yield the wrong critical value.


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Another approach is to use a calculator such as this
https://www.danielsoper.com/statcalc/calculator.aspx?id=4


Want to use a TI83 or TI84?
Unfortunately there isn't an inverseF function (similar how there's invNorm), but you can follow the process mentioned in this video
https://www.youtube.com/watch?v=Bes5pTe3C6I



Want to use a spreadsheet?
You can use a function called finv
The template would be
<font color=blue>=finv(area,df1,df2)</font>
So in your case you would type in
<font color=blue>=finv(0.025,2,18)</font>
Don't forget about the equal sign up front.


Check out this page for the documentation of the finv function
https://support.microsoft.com/en-us/office/finv-function-4d46c97c-c368-4852-bc15-41e8e31140b1


Further Reading
https://www.statology.org/one-way-anova/
https://www.itl.nist.gov/div898/handbook/prc/section4/prc433.htm
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