There are various "tricks" you can use to help you multiply. Here are some examples.
If you can multiply by 2 easily enough, then to multiply by 4 you multiply by 2 twice; to multiply by 8 you multiply by 2 three times. Example: 8*43: 2*43=86; 2*86=172; 2*172=344.
To multiply by 9 you can multiply by 10 then take away the number you are multiplying. Multiplying by 10 just means adding a zero. Example: 9*17: 10*17=170; 170-17=153.
There are various way of making subtraction simpler. You can use chunks. Example: 170-17: take away 20 first then add on 3: 170-20=150; add on 3: 153. Example: 123-89: take away 90: 33 and add on 1=34.
A good way to check if you have the right answer is to use the digital root or nines remainder. You take each number in the arithmetic and reduce it to a single digit by adding up all the digits in the number. If you have more than one digit in the result, just add the digits again until you have a single digit. Example: 12345 has a digital root of 1+2+3+4+5=15, 1+5=6. So the digital root of 12345 is 6 (which means that 6 is the remainder when you divide by 9). Suppose you want to multiply 8 by 43. Reduce these to their digital roots: 8 and 7. Multiply 8 by 7: 2*7=14; 2*14=28; 2*28=56. 5+6=11 and 1+1=2. So the digital root of 8*43=344 and 3+4+4=11 and 1+1=2. This is the same number as we got by multiplying the digital roots and then finding the digital root of the result. This gives you confidence that you got the right answer.
Now, let's use the digital root for 123-89. The digit roots are 6 and 8. 6-8=-2. Whoops! Negative! No worries, just add 9=7. So the digital root of the subtraction is 7, and 34 has a digital root of 3+4=7. This helps to confirm that 34 was the right answer. Another trick in finding the digital root is that you can ignore 9's or any digits adding up to 9. Example: ignore 9 in 89 and we're left with 8.
There are many more tricks, but there isn't enough room to show them all. It does help if you know your times tables, but you can still use the tricks to help you.